I wrote and drew a children's book for a kid's birthday recently (got it printed out by blurb.com). It took some time to do (actually probably about 10 hours drawing/layout time now I think about it) and to think up a story, but I think it was very much appreciated, and it's a fun thing to do. We did one for another kid at birth too, although that was hand made, which was quite an effort (probably well over 20 hours work in that one) – if you do a digital rather than hand-made one, they don't have to worry too much about kids messing up your lovely handiwork either, as it is easy enough to print off a replacement. Obviously a 1 year old won't be able to read text yet etc., so you'd need to make something very very basic, but if you make the pictures interesting, and text for parents to read out, you have something that can last a bit.
Have done similar for a few friends getting married too, although there are less rude jokes in the children's books than in the marriage books, and fewer octopuses and elephants in the marriage books.
I am a big fan of making stuff, particularly for people/kids that you know well, so you have a good chance of pitching it right.
Joe