I've gotten some great suggestions for products just from reading these replies, so I need to first say thanks for posting this question! My daughter is 4 now, and the exact same thing happened for us. It surprised me because my mom had all bald babies, so I had zero experience with baby hair!
I'll add my product suggestion to the others just because I love it and have looked for so long to find something that works! It's by John Frieda and it's called Root Awakening Detangling Spray. I spray it on after her bath and comb through. Her hair is now to her elbows, and there is a part that STILL manages to get gnarled and tangled no matter what! :)
http://www.johnfrieda.com/products/product_detail.asp?pro...
As for how I kept it out of her face, I did bangs for a time, but could not keep that up - she hated getting them cut, and I found that once they grew out, it was easier overall just to pull them back with the rest of her hair. I did the "Pebbles" top-knot on a regular basis and it seemed to bother her the least of all the pulled-back styles I did when she was so young. Barrettes were almost always pulled out at that age. I tried using those little ponytail holders that look like tiny, stretchy little "headbands" that they market to babies/kids, but those slide right out of her hair. It's good if you want to remove them quickly, but way too easy for your child to remove, and they only hold a small amount of ponytail. They worked for a short time when her top-knot was teeny, but I soon found that I had to get some Goody ponytail holders. They have some great ribbed kind with a plastic (not metal) connector so they won't break your baby's hair.
Also, when her hair is dry I brush it with a boar-bristle brush. You can find them at places like Walgreen's now for a reasonable price, and they get the tangles out so much more gently than even a wide-toothed comb. It smoothes her hair as well, which makes it easier to handle when I'm styling it. Wish I'd had one when she was your daughter's age!
Best wishes!