You seem very fixated on Drs working hours, very few doctors put their children in nurseries 6 days a week for 11 hours a day. Only 25% of female NHS staff who have young children work full-time. Yes hospital nurseries are usually more flexible with opening and closing times, but I doubt many children are there for 11 hours a day, 5 days a week.
When do you actually plan to spend time with your child? When the child is little they will need to be going to bed at 6.30/7pm. You will then have to get them up at 5am to get them to nursery, that isn’t good for the child’s development.
I really don’t understand why your child will be bored at home with you. Surely you’ll play games with them, read to them, play with their toys, take them to the park, go out for the day, go for a walk, maybe take them to a baby or toddler group. They shouldn’t be getting bored spending time with their parents.
Even if you do miraculously find a nursery that starts at 6am, you won’t find wrap around care for school age children starting that early. Appart from anything young school children get extremely tired and getting up at 5am every morning will affect their development. Also what do you plan to do with your school age child on a Saturday?
You and your husband really need to look at your jobs, it would be much more beneficial for one of you to start work later and the other one to finish earlier so that your child can go to nursery for a more standard 9 or so hours.
Also surely your husband doesn’t work 7 days a week, if he works every weekend he must get days off during the week. Can he not look after your child then and give them a day/days off from nursery each week?