Wow! I can completely understand your concern/apprehension. My dd is 18 mo but really aware and it's obvious that she understands that her friends have dads, so I'm just waiting for her to start wondering where hers is. Hopefully that is a ways away. Still, I've asked a few people about this (my therapist, friends raised w/o dads, friends who raised their kids alone...) and they have shed some good light on the matter.
One friend who's father left when she was 2 mo said that it never really bothered her and she didn't spend much time thinking about it until she was about 19 or 20. Her mom remarried and the "stepdad" is still the man she calls "Poppa". At 20 she met with her bio dad's family (he had died) and said the experience was important to her, but that she didn't feel connected to them and she doesn't visit them anymore. I pray that dd will be this lucky.
The therapist I saw during my pregnancy suggested that I be honest, but not to supply too many details. After all, your babe is half him (at least genetically) and kids will often assume that if dad is bad, I must be too. The other thing she really stressed is to make sure that you let your daughter know that you and the father aren't together because the two of you couldn't get along. In other words, it's not the baby's fault. Here again, kids will blame themselves for lots of stuff (it's the down side of ego-centric thinking).
For our situation I think I'm going to say something like, "Your dad and I tried really hard to get along, but we just couldn't. So you and I moved here to live." If she asks why he didn't move too I can honestly say that I don't know.
Oddly, just yesterday I had posted a question asking for responses from uninvolved fathers, or people who know uninvolved fathers, under the Dads forum. I'm hoping that the responses can help me see this more clearly. (I don't think that dds father is a bad person, just scared, immature, and totally unprepared for fatherhood. Still, I have a hard time understanding how he could not want to know her.)
I hope this helped, or at least gives you a starting place. Good luck, and remember that your family of two is strong enough, and big enough, to fill her life with love.