Another difference between children that I will just mention is willingness. DS1 is 8. I am sure that mechanically he is perfectly capable of doing dishes and laundry, etc. But emotionally he is not, he is not willing and I think that's mostly because frustration is so difficult for him. But we do insist that he do SOME stuff and even though he still fights us on it 95% of the time, it is good for him to have to because he learns (gradually) that he actually IS capable. Every day he has to help clean up the floors at night (our house is very open and toys go everywhere - kids don't have rooms or even a playroom to contain them). He also often feeds the dog and walks the dog (he is a physically big 8 year old and nobody is going to mess with someone with a 50 lb dog in our neighborhood). He is also capable of clearing the table, emptying the tub (our shower arrangment leaves much to be desired and has no drain currently), putting in a load of laundry, putting away dry dishes, starting a fire in the wood stove, carrying in wood, etc. He could do dishes but he takes forever so usually I prefer to do that myself.
DS2 is 6. He isn't allowed to walk the dog by himself (he's lighter than the dog!) and he's not really physically capable of emptying the tub, but he can do most of the other stuff his big brother can. He is also a much more detail-oriented, organized kind of person so he is also able to put clean clothes away and will sometimes demand that I let him put the dishes away because he'll put stuff where it actually belongs whereas DS1 is more haphazard.
DD is 3. She CAN tidy up toys although she doesn't like to. We're just starting to work with her on actually helping out with that. She also likes to feed the dog, although she needs help to get the rodent-proof bin of dog food open.
Just sharing to give some ideas of what real live actual not terribly naturally helpful kids might be able to do.
Nkhkl - might there be a local teenager who would be willing to come in and be mothers' helper for an hour a day for the first week or so? I agree that you know a lot about dealing with the newborn period and that recovery from a vaginal birth will likely be easier than recovery from a c/s, so I don't know that you especially would need a dedicated post-partum doula, even if you could find one. But a teenager who you could pay a nomial fee to for some minor household tasks might be worth his/her weight in gold . . .. I think that is what I would do if I didn't have the kind of support I (very, very luckily) will have.