I think it if absolutely fine to go back to work at 4 months. Not so long ago the materbnity laws were such that you had to go back to your job at 18 weeks. So lots of people do it with no ill effects.
I went to work FT when dd was 3.5 months old. It was absolutely fine. She is now 15 and I have been working FT ever since. It is fallacy to say that childcare has a long term effect tbh.
It is also about personal decisions. If you want to stay home, fine, but DD's father buggered off when she was 3 months old, if I didn't get a job I would have gone on benefits. And I didn't want that. I wanted to earn my own money.
It has paid dividends, I now have a fantastic career which I frankly wouldn't have had if I stayed at home for a couple of years. And I have a very close relationship with dd - yes you can have both.
Practically speaking - pay as much as you can for childcare. I was skint for years as the childcare was more than my rent. But it was worth it. DD went to a childminder who had 2 mindees (plus 2 school aged children of her own) and DD was there for 5 years. She was very loving and dd is still in touch now. Personally the only nursery in town at the time was rather regimented, I much preferred the home enviornment of a childminder. If you can afford a nanny all the better.
I EBF and gave up when I returned to work. This was a shame however I couldn't express - I used to get a thimblefull after ages of expressing - so dd went on formula when I went back to work. It wasn't really possible to express at work 15 years ago, however times have changed and you will be able to do this now if you still want to BF.
Sleep - yes you will be knackered until you get used to it, but your DH will have to do 50-50 with night wakings.
I have no regrets - going to work was the best for my family in all respects. I was having a conversation with DD about it and asked if she regretted my working FT all through her childghood. She just looked
at me and said that she would do the same herself with her children.
I may possibly be pregnant now (fingers crossed) and I plan to do teh same - back to work at 4-6 months. My career is such that I cannot take time out for any length of time - evwerything moves and changes so fast - so this is the best for me. I would probably do a 4 day week, DP would do a 4 day week as well so childcare for only 3 days. And I think there is no problem with that.
Good luck with your decision, but don't feel guilty. Taking this job will probably make you happier than sitting at home thinking 'what if'.