I nursed my daughter every night between midnight and 1:00 and again at 5:00 a.m. until she was 12 months old, then she dropped one of the feedings, then at 13 months she dropped both and slept through. We had no crying, everyone slept fine and was happy. I went to bed earlier if I was tired. A 10 month old is not guaranteed to sleep all night long, many don't. Very likely by 5:00 a.m. she IS hungry.
There is also no rule that a baby needs to stop formula at exactly 12 months. After my daughter self-weaned at 11 months, I fed her formula past 12 months, and then gradually mixed it with milk over time until she was drinking regular milk. When she wasn't getting formula, she was still getting a bottle of whole milk, so I don't understand your concern there.
I didn't follow the "rules" in raising my baby, I just tried things until they worked. I fed her when she acted hungry, she had an bottle WELL past age 1, and we tried MANY different things to get her to nap (stroller, car, swing, bouncer, sleeping on her dad's tummy...) She napped almost until she started kindergarten but not without effort from us.
I never asked my doctor how to feed, or not feed, my baby. He wasn't in my home at night. I fed her when she was hungry. Doctors know what books say, I know my own baby.