I leave the pram quite a bit, be sure to leave it in an official pram parking area or a cast member will move it to the nearest one & it can take a while to find it again...
Last April my daughter's pram got nicked from near Pirate Beach

....really hard to work out why as it was a well used old Mothercare pram...certainly not this year's Bugaboo. As I have an annual pass I now check in my own pram at left luggage (free) on the way in & rent a Disney pram for the day once inside (also free).
Pram theft pretty rare it seems, but it does happen & I had to waste 3 hours to leaving the park & make the report to the police at the station for the travel insurance claim

& then they only gave me 50% of the value back as the pram was old
