Tumblwd has the right idea. Gate checking. That's the phrase to use. Ask to gate check your stroller. Do this PRIOR TO BOARDING.
You will get it back nearly immediately after landing, and you will get it returned to you in the same place you left it, in the jetway. You've probably never noticed, but the jetway is not just a long thin hallway. Right near the plane entrance, it widens out into a circle. It's in that wide area near the plane door (but off to the side, to allow others to get past you!!!) where you'll get everyhting (like your child) out of the stroller and fold it up. Then you just leave it there. A ramper (baggage handler) will be up at some point to gather and load the strollers (there's an exterior door to/from the jetway at that end). The process will repeat itself, but in reverse, after you land. You might have wait in that circular area of the jetway (off to the side!!!) for a minute or 3, but some time soon a ramper will be up with the strollers, and then you merrily roll along from there. The stroller will NOT be claimed by Disney's Magical Express.
Since you will flying to and from Orlando, you will surely not be the only party gate checking a stroller. Far from it.
When you get to your DME bus, the driver will load the stroller under the bus, and you'll get it right back when you arrive at your resort.