I started knitting a blanket when I was pregnant with my first, until my mom clued me in to just how many other people were knitting blankets for my baby! I ended up getting about 5 handknit/crocheted blankets!

Instead I made her a tag blanket, like a Taggie:
http://www.taggies.com/cgi-bin/estore/show_entry?index=1I bought some fleece, cut it in two squares (about the size of a handkerchief). I then bought ten different kinds of ribbon, with all different kinds of textures (something furry, something woven, something silky, something velvet, etc.) in bright colors and patterns. I was careful not to get anything that would unravel or come apart. I cut two lengths of about 3-4 inches from each ribbon and folded them in half. I arranged them equally around one of the fleece squares, five loops on each side, then pinned the loops so that they were facing the inside of the square. I pinned the second fleece square on top and sewed all the way around, close to the edge, leaving a space of an inch or two unsewed. I turned it right-side out, so that all of the ribbon loops were sticking out of the square, sewed up the little gap left, and then did a top stitch all the way around again to reinforce it and guarantee that the loops wouldn't be pulled out. I was using a sewing machine and I got the whole thing done during the commercial breaks of a one-hour TV show!
My daughter loved feeling and chewing on the tags as a baby and it was a portable size. I could toss the whole thing in the washing machine (and I did this before I gave it to her the first time, by the way).
Another thing that I made for her when she was a few months old was a nursing necklace (don't know if you are planning to breastfeed). This helped when she was getting a little older and easily distracted when nursing! Now that she's older, it's a dress-up necklace. I got a heavy piece of cording that wouldn't break and threaded some big, colorful plastic beads on it. I had beads that spelled out her name at the very end and some cute animal-shaped beads. It is long enough that, while nursing, she could grab onto it with a free hand.
I can knit and sew, but don't really have the patience for either, so I was looking for quick crafts that would be unique! Good luck!