Recipe calls for a 10 cup soufflé dish. I have a 2 quart... Will it work or do I need to adjust recipe or cooking time?

Check out this site:
https://whatscookingamerica.net/Q-A/bakingdish.htm

Another thing you can do is make a foil collar so the souffle can rise higher than the dish. Looks spectacular. Cut a piece of foil a few inches longer than the circumference of the dish; fold it in half lengthwise; wrap around the dish (it should stand a few inches above the rim); butter the area that will stand above the rim; secure with a paperclip. When souffle is done, remove collar and present/serve immediately.

http://m.epicurious.com/recipes/food/views/Gruyere-and-Parmesan-Cheese-Souffle-103223?mbid=social_mobile_email

You didn't say what the recipe is. Two quarts is only 8 cups, so what I often do in that case is put the rest of the recipe into a 2-cup container and adjust the cooking times fo accommodate both containers.