Hi OP! Not quite the same, but my DH has suffered with ME/CFS for over 10 years now - he's technically in "remission" and is mostly recovered, but still has days where he's exhausted from it. DD was born when he was about eight years into his official diagnosis.
DD is 4 now, but when she was a baby I did most of (all of!) the night wakings etc, partly because DH had to get up for work, and partly because I didn't want him to be more tired than he already was! He was fine with the day to day stuff when he was at home (so at weekends), and as she got bigger he was getting better, so was more able to cope with her being mobile and so on.
We were both a bit worried before she was born, with whether or not he would cope with it all. To be honest, he coped better than I did in the early days! We're having DC2 in a few weeks and aren't so worried this time around, but as I said he is mostly recovered now.
Is your ME getting better, or is it likely to? DH was very lucky - when he was first diagnosed he was extremely unwell, there's no way we could've had kids when he was in the early stages. They gave him 10 years to recover and he had a relapse after 2 or 3 years (so restarting the 10 years again!), but slowly got better. Now it's not really an issue anymore, and we're just keeping everything crossed that he really has recovered. Obviously he isn't the one going through pregnancy/birth, but it's still tiring being a Dad!
Having a good support network (especially a supportive DP) is a very good start. And don't worry about being able to do "what other Mums do" because we're all different. If you've got family and friends, and they eventually go to preschool and then school, they get a wide variety of experiences through that - it doesn't all have to come from you. Best of luck to you 