If they tend to be fussy, I second buffets. - No waiting and people expect noise anyway! But sometimes kids get over-stimulated at Disney and actually enjoy and absorb a quiet spot for a bit, so you may be surprised.
Your best chance at success is all in the prep, though - same as for restaurants at home. Be prepared with things that hold their attention (fairly easy at Disney) and things that calm them (not so easy at Disney). My biggest tip is to include them in the conversation. A meal isn't really your break at that age (I remember really missing that!) and I think it's when parents treat it that way that kids in restaurants tend to lose it a bit.
For the 2.5 year old, you might be able to teach him/her "I Spy" before you go - It's a good game for waiting and a great way to practice colors or shapes. A pad of sticky notes in your bag is simple and small - good for drawing, counting, covering things up and remembering what was there...
The 1 year old will probably just want some quiet cuddles. An air-conditioned restaurant is a great place to reconnect from being in the stroller and sit on mom or dad's lap for a bit before the food comes!
Trying not to let them get overwhelmed/exhausted in general helps too. You know your kids, and what sets them off. If they're content going in, the restaurant will just be more of the grand adventure. So keep close to their normal schedule if you can, and remember that everything is about the "sweet spot" - hungry enough to eat, but not so hungry they're cranky, etc. (I think it's good to occasionally take a little walking break if they're in a stroller all day, too - stretch those little legs.)