Yes, it is possible to trade a studio for a 1 BR. The only way to do this is via Deposit First where you call in and request a studio deposit. You pay 4000-8000 depending on the season. You have no choice on which resort you get. If you get a strong trader, you can use it to book any size it will pull. If you get a dud, you will be lucky to trade for anything except a studio. What week do you have? Note that with a studio deposit, you can only set up an ongoing search for a studio unless the resort you want doesn't have any. To find a 1 BR, you need to do a manual search and will be checking the leftovers. However, whatever you see, you can book.
Most WM to II trades are REquest First. You put in your request using the WM Float (which is a combination of all resorts and is the strongest trader) and you pay the number of credits based on the size and season that you match to. If you want a 1 BR, you would specify that in your search.