Ok, so The Doctor isn't made of flesh and blood but he is still just as much part of the crew as anyone. As long as the child knows who her parents are, I see no problem with a holographic nanny - imagine the fun you could have with the doctor if he didn't have his duties.
I'm sure loads of other crew members would happily look after the baby whilst her parents were at work.
Naomi Wildman? She'd have made an amazing babysitter - she did quite well helping Seven rediscover humanity. How did Sam Wildman cope? Others must have helped.......
Seven of Nine? ok, so she's not the perfect choice, but it'd help develop nurturing - not sure B'Elanna would trust her with the baby, as they were at each others throats when Seven came aboard... but maybe she and someone else could watch the baby.
Surely when the child was older, she could start helping basically - Dad could teach her how to fly the ship, Mum to teach all the technobabble.