In Epcot: You could use the gazebo located in the UK garden area.
Or- You could ask her in the sculpture area in Italy. Any chance of the honeymoon being in one of these real places? Ask her in that land.
Near MK - try renting a boat ride and asking her on board the ship. Then the honeymoon could be a
disney cruise later on a bigger boat!
They have a Wishes cruise I think!
In MK - Tom Sawyer's Island....explore the caves and such...sit on the porch. Or on the train?
MGM- During Fantasmic? (but too crowded I think)
Animal Kingdom - There are many beautiful settings of benches etc in out of the way places.....look for them.
Many of the Resorts have wonderfully romantic spots.....Wilderness Lodge, Poly, GF, etc. You could book dinner ressies for afterwards. Whipsering Canyon or Victoria & Alberts would be great. Have the chef hide the ring in the dessert or something. I am sure they would do this for you.
MHO is that the timing needs to be not "too loud" or busy/distracting. I think a bit more secluded, away from hustle/bustle of crowds would make for a more memorable proposal. The crowds would be distracting and you wouldn't your memory interrupted by a parent yelling at a child, or someone becoming ill nearby, etc.
You could perhaps hint before the ring...by giving her a wrapped present of a mickey minnie figurine of them in the bride/groom outfits......tell her it is for the cake if she says yes.