Hi Ryann!
Thank you for bringing your question to the Disney Parks Moms Panel!
This is a great question and one that we used to struggle with when our boys were little. I do think you will want a double stroller while you are in the park. It really just depends on whether you want to carry your eight-month old (and possibly tired four-year old) out of the parks and onto the buses at the end of the day. The walk to the bus stops can be very long and include a lot of waiting, with more walking once you reach your resort.
Here is a link to a
stroller guide for Walt Disney World. There is information about their strollers, and also some of their "Featured Providers" that you can rent from to keep with you the entire trip. These can even be delivered to your resort.
Personally, I think you would happiest with renting a stroller for your entire visit. The Walt Disney World strollers are great, but not really suitable for an eight-month old baby. You would be better off getting one that your infant will be comfortable in since they will likely be sitting in it for a large portion of the day. Kingdom Strollers has a large selection of stroller types and we have used them successfully in the past.
The website www.wdwprepschool.com has a great review of different stroller companies.
I hope this helps! Please let me know if you have any other questions.