Quoting Jenny Cook:" hello im jenny, im 17 and having a beautiful daughter, i havnt been with her father for the past 5months, ... [snip!] ... and helping me, do i even have a right to say hey buddie be a dad would ya !? seeing its not his kid ? HEEELLLLPPPPP! PLEASEE!"
There's no rules to follow, it's all about what you feel is right. If you're ready to date, then do it.
That being said, I would personally feel hesitant. He may be very happy to be with you right now and intend on being there for your daughter. But it's extremely hard to have a newborn and be in a relationship. It was hard for my husband and I and we had certainly been together for more than a few months. So he may very well decide to leave and I personally wouldn't hold that against him.
But you won't know if you don't try and I think were I you, I would try it. And if he does stick around and intend on being her dad, I would expect him to step up, too. I won't lie, I'd probably feel weird demanding help from someone in that position, but you'd eventually have to work around that.
I would talk to him. You're having a baby, you're about to a mom, and there's a smurf ton of work that comes with that. He really has to think about if that's something he's ready for.