You can get ticks anywhere there are trees and animals. She could have easily gotten it there. But, it really doesn't matter where she got it.
Here's a link to ticks in Florida.
http://solutionsforyourlife.ufl.edu/hot_topics/families_and_consumers/ticks_and_disease.html
Ticks generally stay fairly low to the ground, so dropping out of trees is not common. And, they are more common in areas with underbrush, layers of dead leaves, etc.
The black-legged tick, used to be called deer tick, but their major host animals are actually mostly small mammals - mice, chipmunks, squirrels, and, in warm areas like Florida, lizards.
People see ticks on their heads and assume the tick dropped from a tree, but it's most likely to have gotten onto the body lower down a crawled up (I know, eeewwwe!).
This information is from a talk I went to last week presented by one of the chief investigators into Lyme disease in Minnesota. Ticks often roam around on the body for 12-48 hours before settling down to feed.
And, then feed for many hours up to days.
Maybe people get snarky because they realized that the OP was at the parks having fun and they weren't
PS OP if you are reading, if you happened to save the tick and believe the tick was on your child for longer then 24 hours, you can have the tick tested for lyme disease.
Testing ticks for Lyme disease is a common misconception. Except for research, they don't usually test the ticks. They just look whether it is the type of tick (black-legged tick) that can carry and transmit Lyme disease.
Lyme disease if pretty uncommon in Florida according to this nice education sheet about Lyme disease and ticks.
So, if they brought the tick with them from a place where Lyme disease is more common, there is a greater risk of Lyme than if she picked up the tick in Florida.
Lyme disease is what people think of most with ticks, but they can also transmit other diseases. For Lyme, in general the tick needs to be attached and feeding for 36-48 hours to transmit enough bacteria to transmit Lyme disease.
The CDC has a lot of good references:
http://www.cdc.gov/lyme/
There are other diseases that can be transmitted by ticks, so the OP should be aware of any symptoms that might develop. Tick borne illnesses in general are less common in Florida, so if she picked up the tick in Florida, she is less likely to get sick.
Didn't read all replies but I read enough. Perhaps OP was waiting for people on a ride, in the middle of a show, or even eating lunch and thought they would just pop on and post a question. Most questions on here get a response in under 5 or 10 mins. If that is the case, then where is the harm in asking on here? If the answer was no, it would have saved OP the trip to first aid possibly from the back of the park. So what's the difference? And why is everyone so quick to assume OP wouldn't have asked someone in the park too?
As for first aid, I think some people have the impression that first aid is staffed by a couple college CMs who hand out band-aids and Neosporin and send you on your way. It's obviously not a doctor's office or urgent care and if you've never utilized a first aid stop somewhere, how would you know? I would think liability would play a factor too. Of course it never hurts to stop and ask, but if you think of first aid in this sense, whether or not they would help with a tick is a fair question. I would have expected to be sent to urgent care.
I just want to clarify that at WDW, First Aid is staffed by Registered Nurses and they are working under protocols to treat common things.
For more severe illnesses or situations that dont fall under the scope of their protocols or the practice of Nursing, they will suggest the guest go to Urgent Care for non-emergency situations and EMS/paramedics will come to the park for more emergency issues.