I've used my power chair on two trips to Disney (one to California, one to Florida) and I'm planning to take my chair on all future trips. On both trips I had connecting flights, so I've had 4 flights total round trip. The airlines didn't cause any damage to my chair (which is EDIT: quite similar to the one you have).
Now on to statistics - the latest info I could find (from October 2021) indicates airlines damaged an average of 29 wheelchairs/scooters per day. The latest statistics (from 2019) indicate airlines transported more than 685,000 personal wheelchairs in 2019. So the statistics say your chances of damage are pretty low - roughly 1.5%.
Now if your chair does get damaged, there's a
good article at wheelchairtravel.org on what the airline is responsible for.
"The good news is – if an airline damages (or destroys) your mobility equipment, they are on the hook for 100% of the repairs, up to 100% of the original purchase/list price. They’re also expected to accommodate you with a loaner chair for as long as the repairs take. My replacement wheelchair came within 2.5 weeks, which I felt was pretty fast for a complex rehab power chair."
Orlando has many
ECV vendors, so this should improve the chances of you getting a loaner
scooter for your time there. The chances of getting a loaner power chair are much lower since not many vendors rent them.
If you decide to take your own chair, read the rest of the article I linked. It has great advice on what to do if your chair is damaged, plus a link to another article on how to reduce the risk of wheelchair damage by the airlines.
If you decide you would rather rent a scooter in Florida than take the chance of damage to your power chair:
For transport through the Orlando airport, you can request wheelchair assistance from the gate. Or if you prefer to bring a manual wheelchair with you and have someone in your travel party push you, you can buy a cheap wheelchair.
When you get to Sunshine Flyer let them know you need to take your time on the steps. Or if you have a manual wheelchair, the bus should have a lift so you can stay in the chair and avoid the steps. You can confirm with Sunshine Flyer that the bus has a lift now if you haven't already done so.
You may have read the many discussions here about which scooter vendors people prefer. Gold Mobility seems to get a lot of good reviews. The one thing I would do is avoid ScooterBug. I have heard too many stories of bad experiences with them (equipment issues and inadequate customer support). Plus, their speed is purposely throttled down when compared to Gold and basically any other outside vendor.