Hi there. First I'd like to say, you can't underestimate how hard those first four months are... The first year really but especially the first 4-6 months. Anything you do to get through them is worth giving yourself some massive kudos for. And when your relationship is unstable too, seriously, that can be so lonely and exhausting...
It DOES get better, whatever happens, it gets SO much better than you're probably feeling right now. You'll be able to look back through the sadness of how it feels at the moment, and still feel overwhelming joy at the amazing moments you spend with your baby.
I'm saying all this because it's what happened to me. I moved across the country to have a baby with my partner (at the time) but by the time our son was 4 months we were on our last legs, by 8 months it was a nightmare and by a year I'd moved out to live with my parents while I decided what to do.
I've got a number of friends in similar situations and what I can say from my experience and those around me is, everyone does it differently and I think it's important to get a good gauge of what you need, what is practical, and what your child's Dad is willing to do. Discuss it as calmly as you can and be willing to be flexible over time to make it work. And don't compare your situation too much to others coz that can be really painful.
My son's Dad has him Fri/Sat night every other weekend, and then every Wednesday evening just for bedtime, drops him off in the morning. The rest of the time he's with me. When he was very tiny I actually stayed over while he was with his Dad ... but that was largely to do with the distance. Another family I know, the childcare is shared 50/50. Another, it's flexible, they discuss which days they're doing from week to week, and the grandma takes the child a lot too. It can be easy to look at others and wish it was different but in the end there will be a balance that suits the situation- not just on a practical level but something that suits the requirements of the relationship you have with the baby's Dad. I think the more friendly you're able to stay, the more involved he's likely to be, from what I've seen.
And that in itself can be a difficult one- staying friendly whilst breaking up. You're always going to have a relationship now that you have a child together. It can be a good thing actually- to remain friends because once you've had the kind of love that forms a marriage and a baby- you've created something deep there. It doesn't just go away. Sometimes you can really care about a person and love being around them, but being a family together just doesn't work no matter how much you want it to.
However the other thing I'd say on that point is- it doesn't have to end just because you leave. When I left I told my partner it was because I physically couldn't be there any more- it was making me ill, but I also believed with some space and time we could make changes and compromises if we were both willing to hold on to what we had.
For us, it didn't happen- we broke up- and in hindsight (5 years later) I know exactly why, but at the time that space helped get perspective. I think if we'd been able to, we'd have pulled it back together then. Having a small baby is incredibly unsettling to a relationship, even a strong one!
Take one thing at a time, give yourself love and not too much grief. I held SO much guilt for such a long time. My son's Dad helped me feel it even more in the things he said at the time. But friends and family kept me strong and (reasonably) sane. I also got a talking therapist who guided me through the healing process after it all. I'm so grateful now for every person who helped me back then.
My son is a super happy, super confident little person. He breezes through the process of living in 2 places and has no memory of any of the break up. In a way I'm glad it happened when he was so young.
The hardest part is what you're going through now. Happier days are coming. Sending so much positive strength your way!! x