Just a personal suggestion... until you have your issues with your ex, custody, visitation and how you all work together, I wouldn't even contemplate marrying someone else.
Just for you, from a woman's standpoint, it's not an emotionally healthy thing for you to do, particularly when you have a lot of unfinished business in your previous relationship.
I married a man almost 3 years after his divorce, and he had a child. One would have thought after that amount of time, they'd have some semblance of closure, but they did not.. Or he did not... Or maybe she did not either. Who knows.
Anyway, what started out as an idyllic relationship (and was quite a bit longer than yours sounds like it is here), went to [censored] pretty darn quick when all the baggage started arriving on the metaphorical carousel of life. Now we have a 1 year old ourselves and are now divorcing.
Take some time, slow down.... if the guy loves you and wants to be with you, he'll understand and wait until you're in a better place.
As for "x"ing your ex out of the picture. You're not THAT far out of your divorce and being newly separated myself, I can relate to having that feeling, and have to remind myself that regardless of whatever my stbx did to me, as a wife, or even to his daughter, as a father, in making the choices that he did... that she's still got his dna, he does love her... he's just incapable of being a mature, responsible partner in a relationship. However, he is a caring father (do I agree with all his philosophies or parenting traits? NO, but then he doesn't agree with 100% of mine either).
Now, if he ever puts her in position to hurt her emotionally or physically, I'll be all over that like white on rice... but until then, he is her family, as much as I am, and whatever my issues are with him as a man, I have to separate them from my feelings as a woman.
Okay... thanks to all here that beat that into MY head... and typing it here was as much a message to you as it was a reminder to myself :)
PS: I strongly recommend counseling as well. I am in the process of locating one for myself for my situation and dealing with my resentments towards my stbx so they don't affect our daughter going forward. Divorces can be hard on self-esteem.. Sounds like your self-esteem tank might be a little low.. god knows I can relate to that! Counseling might help you see things more clearly going forward.