Hi Jill, and welcome to planDisney!
The question that you ask is one that I had when my children were younger, and unfortunately, you are unable to reserve a stroller ahead of your arrival. The good news is that there are plenty of
strollers for rent at each theme park and Disney Springs, so I am pretty sure they will not run out, especially if you arrive early in the day. Remember that if you need a stroller at different theme parks in one day, just pay for the stroller at the first theme park, return it on your way out, arrive at the next theme park, and show your receipt. Renting a stroller at Disney Springs will be separate.
If you want access to a stroller outside the theme parks, the Disney Featured Provider, Scooterbug, is a great choice. We have previously used them for wheelchair rentals, and they delivered the equipment to the resort before our arrival and picked it up after we checked out. That same service is available for stroller rentals.
We will be here if you need us; please let us know how we can help.
Have a magical day!
Raquel