F/T Nanny here: I would also consider relaxing this schedule a little bit. It's not that it's unreasonable, but as a Nanny I have worked for families with a schedule similar to this and worked with families that just gave me their expectations for the day and then let me figure out what worked best (for toddlers, obviously infants need more of a schedule). I much prefer it being up to me as I think we are able to have more fun that way. I can push nap time up or down an hour so that we can go peach picking, or combine quiet time and outdoor time on a nice day by taking a blanket and books outside for a nice reading session. Also, obviously nannies are there to meet your expectations and make you and your family happy however, (for me at least) it can rub a nanny the wrong way to be told what to do every minute of the day. It sort of makes me feel like you don't trust my judgement and ability to plan a fulfilled and fun day.
I much prefer what the first PP said, "I like them to spend at couple hours outdoors, a few hours reading and some educational activities and lunch time / rest time is normally around 12PM".
Again, I don't think your being unreasonable, just giving you my opinion.