There are actually several EDSers on the boards (I'm one - I also have Hypermobility type). I'm a wheelchair user most of the time I'm outside the house, anyway, so I use my wheelchair, although, I have to get pushed in WDW because I can't wheel the entire distance, can't use an
ECV (my hands/thumbs are particularly bad) and since diagnosis I haven't stayed on site so couldn't transport a powerchair.
I guess my big concern would be how many people are in your party and how you plan on getting around the world. Most people walk a minimum of 6 miles a day in WDW and depending on where you tend to have problems, that could be more than you can easily handle. I would really think about whether you and your daughter can handle that much walking on repeated days and possibly consider getting a wheelchair (either of you) or ECV (just you as you must be 18 to rent). WDW's answer to mobility and stamina issues is to suggest you rent one or both as there aren't benches in waiting areas and on paths where there are benches they may be full.
I'd also suggest you think about what rides might cause problems. For example, when I was last at Disney, I could ride Rock'n'Rollercoaster, but not Space Mountain because Space Mountain didn't give enough back/neck support, but RnR gave me enough. If you're extra prone to issues with bumpy things I know Kilimanjaro Safari was one of the bumpiest rides I've been on recently, but even Haunted Mansion and Spaceship Earth feel bumpy to me.
Other tips I'd have are:
1) Make sure you have enough pain medication. I would plan in needing extra meds just in case. I know even being pushed in my wheelchair I tend to need extra pain meds.
2) If you can, taking a break during the day (either you can lie down in a First Aid center or go back to your hotel if you're close enough).
3) Drink plenty of water/other fluids. If your dysautonomia is acting up Gatorade is good, but make sure you're getting plain water as well because even Gatorade will dehydrate you.
4) Don't plan to do everything. Even commando-type touring rarely means you can see everything and you can always come back to WDW again someday!
5) Remember that it's better to slow down, look at using a mobility aid, and enjoy WDW than it is to suffer through pretending you don't have EDS so that other people think you're normal. No one outside your party there knows you or will care if you and your daughter can't walk the park and it will be more fun for your entire party if you're not struggling and miserable in pain!