First off, I hope you both have a fabulous time!

Second, this is a challenge

that I am happy to try and tackle; romantic and quiet but not signature, I'll think hard.

And now, some suggestions:
MK area-
Kona- Not a very quiet place, but it has IMHO potential for a great romantic breakfast (especially if you go after the park has opened and it's not as busy)
Grand Floridian Cafe- Anything at GF is going to have a touch of romance, but this location (especailly for lunch) is often overlooked and thus has a better chance of being quiet
MGM/DHS area-
Mama Melrose- This is a controversial choice because the merits of this location are constantly debated on these boards, but I still believe that it could be a quiet and romantic location if timed correctly with a late dinner
Sci-Fi- This is more of a playfully romantic location that is also rather controversial for the foodies, but come on, who wouldn't want to relive some of those teenage backseat makeout sessions?
Fresh- This one is at the Dolphin hotel but has a quiet no kids area that you can request for a quiet relaxing brunch or lunch
Kimonos- At the Swan, as long as you get there before the karaoke (unless you want to be serenaded by your beloved

) I'd also recommend this location as a nice place for two
Epcot area-
San Angel Inn- Controversial yet again, this location isn't everybody's cup of tea, but if I were trying to have a romantic evening it's where I would go. Nothing goes better with romantic passion than spicy food and low lighting
Teppan Edo- Nearly always quiet and if you get a table overlooking the World Showcase Lagoon it could very well be romantic as well
Chefs de France- I would recommend getting the first table of the day for a quiet and romantic lunch
I sure there are many that I've left out, but here's a start.