Hi Bernadette!
May is a beautiful month to visit Disney World. The weather is warm and sunny, while not being oppressively hot. Epcot is hosting its annual International Flower and Garden Festival that is magnificent and definitely worth a visit!
As for whether to rent or bring (buy) your own stroller, I'm a big fan of bringing one. Renting a double stroller currently costs $31 per day. If you get a "length of stay" rental (which will cover your entire trip), you can save a bit and pay $27 per day. If you "do the math", in most cases, it's less expensive to purchase your own stroller. In addition, you'll be able to use it outside the parks in places like the Boardwalk and around your resort. My children wouldn't be caught dead in a stroller at home (two boys, ages 4 & 6), but we still bring a stroller because everyone in my family is happier when their legs don't hurt from all the walking. A stroller also makes it convenient to maneuver around the parks at an adult's (rather than a four-year-old's) pace!
As for what type of stroller to get, I would ensure you check the weight limitations to ensure they can accommodate your six-year-old. We got a lower-end side-by-side Maclaren about two years ago, and each seat holds up to 55 pounds. The stroller is very light and folds up really small. I've taken it when I've gone to Disney alone with my boys and it worked great. Another good place to pick up a stroller is at local garage sales and online auctions. In fact, I regularly see stroller listings that say, "used once for a trip to Disney."
If you decide renting works better for your family, feel free to click
HERE for additional information and rental locations.
Have a wonderful trip!