Hi M..
My girls were barely 6 and 3 when my ex-husband and I separated. They're now 8 and 5, and they haven't heard from their dad in about 18 months. We don't know where he is, and neither does his family (who we've remained close to). He has essentially fallen off the face of the Earth.
In my case, my girls remember their dad (especially my oldest), and they periodically ask about him. Your daughter will likely ask when she gets a little older, too. In the meantime, I agree that you don't need to force the conversation. Anyway, I tell them that their daddy loves them, but he isn't well enough to be a good dad to them. (He's an alcoholic, and they know this about him.) I also teasingly say that I'm glad I don't have to share them with anyone.
I've learned that kids are very observant and intuitive, and you really don't have to say a whole lot to them. They'll get it on their own sooner or later. Here's an example of what I mean: I'm engaged to a wonderful man who has been in our lives for about 2 years now. He has 4 great kids of his own, and he has eagerly accepted the role of "dad" to my girls as well. Last weekend, my oldest daughter spontaneously started listing all the good things about him. At the top of her list was the fact that he's honest, he keeps his word, and he's always there for us. She recognized - on her own - how important these qualities are. I asked her if she feels the same way about her dad, and she said no. She said she loves him, but she doesn't really know anything about him. Enough said.
One last comment regarding another mom's response: If your daughter's father agrees to relinquish his parental rights, he is also relieving himself of his child support obligations. Of course, if you're not getting child support anyway, it doesn't really matter. Just something to consider.
Good luck to you. Being a single mom isn't easy, but it's a whole lot better than staying in a bad relationship. :)