Yes, reservations are a must! Give Central Reservations (CRO) a call at (407) W-DISNEY. I've read on other posts that sometimes when folks have been told FW is full, to call back every morning to see if that's changed because the computer refreshes the system every night and thus any cancellations will show up as availabilities the next day. It's not out of the question that FW could be booked full this time of year!
As for tenting in general, when you make a reservation, you may have to settle for a full-hook up site, depending on what's available (there are only 2 "tenting" partial-hook up loops, and I don't think either of those are designated pet loops anyway). Make sure you let the reservationist know that you will be tenting so that you can hopefully get a site with a larger sand pad (as opposed to a larger concrete pad, which is better for a big RV). Yes, also make sure that you have a vapor barrier under the tent (visqueen, tarp or similar plastic). Sleeping pads help with warmth and comfort, too!
Good luck and have a blast!!