This is almost exactly my situation, I couldn't conceive with my exH but fell pregnant straightaway with the rebound.....we split soon after I found out and I didn't think he'd stick around but he absolutely has and we have a brilliant co-parenting relationship. Our DD is our sole focus and we don't have any shared history that makes things awkward - it's actually so much easier (I can't imagine seeing my exH every other weekend, that would be awful). We had a wobbly start and there were solicitors involved, but time heals and we've found our groove. I was diagnosed with breast cancer 2 years ago and he moved into my house to look after our DD while I was too unwell, and last week I went on a work trip and he came to stay and look after DD and my 3 dogs. We're great pals - but nothing more!
I would say if you want to go ahead with the pregnancy then do, but you have to be prepared to share your baby - and that means overnights etc. My DD went for her first overnight at his when she was 4 months old, although he'd had her for a full day in the weeks running up to it....I was still BF and sniffing her clothes to pump when she was away so eventually I had to stop when she was 6 months old. I wasn't happy about her going, but I knew it had to happen eventually so the sooner the better. He stayed with his parents the first few times he took her overnight so I knew she was being cared for properly and at the end of the day, we both love and adore her and he isn't going to bring her to any harm, and I've learned to trust him with her. Now she's 8 years old and loves her time with him, and it's really healthy for her to see us getting on and we always do a joint birthday and Christmas. (Maybe it helps that neither of us has met anyone else, but we make it as easy as possible) In the early days he relied on his parents a lot for help and support with her but as she's got older he is now very much in charge and they love their time together, he has taken her on holiday by himself a few times now which I encourage!
He does drive me mad sometimes, but who doesn't? He always pays maintenance on time, and he is always there for her - comes to every parents evening, brownie promise, first day of school etc....but he's very clear that apart from the occasional extra like last week, and school holidays he doesn't want her any more than every other weekend - but that's ok, I couldn't imagine her being away more than that anyway.
Also hormones make you crazy, so try and have someone you trust on your side to tell you when you're not acting rational - because I did a lot of things I regret (I didn't tell him when I was in labour, and just announced the arrival afterwards, and I registered her without him and then had to go through so many hoops to add him at a later date), and I wish someone had told me to behave!