We camped without a car recently.... worked out well. We signed up for an Owner's Locker and will be keeping the majority of our camping gear in storage, for easy travel in the future. The advantage of this, too, is you are supplied with a fairly good size plastic bin, to store things securely in while camping, then pack up your gear in, to have shipped back to the storage facility by the "purple van" of Owner's Locker. It is remarkably easy. We store our UL 6 tent, bags (compressed), utensils & cooking/eating supplies, electric blanket, electric heater, hygiene items, etc. What we bring home is the pads for our bags, as it's suggested they are stored open and spread out, but they fit in a carry on.
It is an EXCELLENT way to camp! We kept our food in it while at the parks and cooked out for lunches and dinners (cereal for breakfast). The top of the OL snaps shut, so it keeps out the wildlife of WDW. Good luck on your trip!