It's the same as at any other studio in any other dvc resort. It goes from floor to just under the counter. I'm sure you can remove a shelf to fit a gallon in there.
I was impressed with the size of the refrigerator in our studio. But I think we purchased half gallons just so we could fit other things around it, as gallons are more rounded than flat on the sides. But we bought enough food for a week(breakfast and lunch) and everything fit just fine. It was great!
When we stayed in studio last May, I purchased the half-gal. size because of spacing of other items we needed to have in fridge. Plenty of room, but just need to be a little creative in how you put things away.