The QS, Gaspy's, does a terrific job! I'm dairy and gluten intolerant, and they feed me nicely indeed.
As the prior poster indicated, food courts are not a Deluxe thing.
What to be aware of at Gaspy's is that if the mobile ordering menu doesn't cover your kids' allergies, you won't be able to mobile order.
You'll need to go in and talk to a CM, telling them you need allergy ordering. When we were last there, it was a CM at the bakery case to the left as you enter who handled ordering for allergies. That was over a year ago, though, so it may be done elsewhere by now.
The allergy-UNfriendly menu is bizarrely organized anymore. (Scroll waaaaay down to the bottom of the Gasparilla Island Grille menu on the Disney site, not AllEars which doesn't list the a-f items.)
If anyone has more than one allergy or any not regarded as common, it's tons easier to go into Gaspy's, ask for where to allergy order and simply tell the CM what you need. They'll help figure out what menu items can be made safe.