Step1
Body and head shapes for the New Year Baby
Practice small until you get a good smooth rendering of the New Year's baby. It helps to draw any cartoon more than once to get used to the design, so now is the time to make place cards, invitations or greeting cards before tackling the big poster.
My examples are all in ink so that you can see them easily. Light blue lines represent pencil lines and black lines show where to go over the pencil lines with your black marker.
Start with a circle for his head. Do an oval about like two of those circles for his body. Then start adding smaller ovals for his thighs, calves, upper arm and lower arm, finally small ovals for his hands and feet. Don't worry about the hat yet. This is just the body worked out in easy geometric shapes. Try this as a doodle a few times till your proportions look like my example.
Place his head about a quarter of the way down the page to leave room for the hat and the whole drawing.
Step2
Hat, diaper and martini glass sketched
Sketch in his hat, diaper and martini glass. The hat is the tricky part. You're doing concentric ovals that fit over his head, flattened ones that make the hat look three dimensional. Go ahead and sketch over it a couple of times till you get it right, I did. Right now the sketch looks like the transparent gelly baby with a transparent hat, but soon you'll ink the cartoon and it'll all make sense.
Top hats have a contrasting band, so we want the brim of the hat to fall below the edge of the hat band so it can be seen. Draw a cylinder by drawing an oval at the top and an oval that just fits the head and connect with two vertical lines. Then draw a wider flattened oval for the brim and another oval a bit above the one on the head to make the hat band. Adjust till they fit naturally.
The hat should angle a bit to one side or the other like the baby's pushed it back and might be wobbling.
For the diaper, draw loose curving lines around his tummy and crotch, then put two little ties on either side. Alternately you can fold it over and draw safety pins on the sides, or make him very contemporary by putting tape tabs on the sides of his diaper. I went with an old fashioned cartoon version.
The martini glass is just a triangle point downward, a stem and a flat bottom that would be a shallow oval if it wasn't exactly side-on to the viewer.
Step3
Face, hat and head inked.
Now let's start inking the little fellow!
I put the features on without sketching them first, since there were so many sketch lines in the area where his eyes go that you wouldn't see them. But you can erase the sketch lines within the head except for the line where the brim of the hat actually touches his head, and pencil in his features to get them right before inking them. I recommend that.
Draw the hat first. Color in the brim of the top hat solidly, when inking the cylinder of the top of the hat curve it slightly indented as shown. Draw the line of the hat band and then above it, color the top of the hat except for a shiny highlight bar toward the right. You can put a narrower highlight on it too, but I like just using one for drama. This makes the hat look shiny. I didn't color in the band, you can either shade that with hatching or leave it white for contrast.
For eyes, I did two shallow curving lines under them to show a baby's rounded cheeks, then a half circle over those touching them. Inside that, I did the iris of the eye looking off to the right, leaving a little white highlight on the iris. If we wanted more detail, outline the iris, put in a pupil, and put the "catchlight" on the iris crossing the pupil and the iris, a little to one side. The "catchlight" is what makes eyes look shiny either in cartoons or realistic drawing. It makes them obviously eyes.
The nose is just a little upturned curve a bit down and between the eyes. The mouth is a cartoon mouth, with two curves at the sides of a big wide smile. He's having a good time!
Add two little eyebrows above his eyes -- little ones, he's a baby. Don't give him a thick monobrow unless you are making him a caricature of someone you know who has a monobrow. Put one ear showing on the right at about the level of his eyes, it can be as simple as a reverse C.
We'll ink and detail his body in the next step.
Step4
New Year Baby inked with sketch lines showing
Erase any of the overlapping marks from the construction ovals that get in your way, if you want to do details like the hand. They're there for reference. It always helps to pencil details unless you've been doing it so long that you don't need to.
Go to the outside edge of your sketch lines to make him plumper, and put little elbows in where they show. Do his hands very tiny and plump with short fingers. Copy the hands carefully. Babies' fingers are very short in relation to the palm, but make sure you have four fingers and a thumb arranged the way they are in my drawing or he may look as if he's got unreal hands.
On the hand holding the glass, first draw the thumb going over the stem of the glass. Then put his fingers curling around to meet it, and the flat bottom of the glass crossing them. His little finger is a bit obscured by the bottom of the glass, but it's there. Outline the stem and curve the sides of the wine glass a little so that it becomes a wine glass. Put a couple of small bubbles in the wine, and draw the oval of the top completely as it's tilted a little forward. Draw bubbles floating up from his champagne.
On his diaper, go around your sketched lines to the outside of the line and draw a knot where it's tied on the sides with a small circle and two pointed ties sticking out of it to the outside. Draw a couple of creases to show how the cloth is folded and bent into the diaper.
On his thighs, show his knee dimples by continuing the line of the outside of the thigh a bit past the point where it meets the next oval. His legs are a little bowed because babies' legs really are that bowed, and his feet are short and fat with very small toes. Copy or trace my drawing if that helps.
Erase all your sketch lines, and you're finished! You can color him in pink, light beige or brown, but if you color him on the poster, do the coloring before you use the black marker to do his outlines. Black marker bleeds into colored markers and can give him unintended gray streaks if you color him later. Make the champagne pink if you color him and make tha hat band gray -- but not the highlight on the hat. Here's how he looks with the sketch lines in place.
New Year Baby traced and colored
Body and head shapes for the New Year Baby
Practice small until you get a good smooth rendering of the New Year's baby. It helps to draw any cartoon more than once to get used to the design, so now is the time to make place cards, invitations or greeting cards before tackling the big poster. 
Hat, diaper and martini glass sketched
Sketch in his hat, diaper and martini glass. The hat is the tricky part. You're doing concentric ovals that fit over his head, flattened ones that make the hat look three dimensional. Go ahead and sketch over it a couple of times till you get it right, I did. Right now the sketch looks like the transparent gelly baby with a transparent hat, but soon you'll ink the cartoon and it'll all make sense. 
Face, hat and head inked.
Now let's start inking the little fellow! 
New Year Baby inked with sketch lines showing
Erase any of the overlapping marks from the construction ovals that get in your way, if you want to do details like the hand. They're there for reference. It always helps to pencil details unless you've been doing it so long that you don't need to. 
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