Hi, Sofia!
Welcome to Walt Disney World! That is awesome that you are traveling all the way from Sweden. What an exciting journey you have to enjoy.
You are certainly welcome to bring your own stroller. If you would like to
rent a stroller at Walt Disney World, these are only for rent inside the theme parks and Downtown Disney. The strollers may not be taken back to your resort with you.
If you are looking for a length of stay stroller, you may want to look to an outside source like OrlandoStrollerRentals.com or other independent company that will bring the stroller to your resort. You will have it for your entire stay, including at your resort and for walking to and from buses, food courts, etc.
One final option is to buy a stroller once you arrive in Walt Disney World. Most resort gift shops and parks will sell "umbrella" type strollers that are very nice for around $50 (prices subject to change). These are single strollers, so bring your own or use one of the other options if you are looking for a double. This will be yours to keep, so you can take it on buses and back to your resort.
There is a lot of walking at the parks and at Art of Animation, so if you have little kids, a stroller is a necessity. You will just need to decide what type is best for you! Good luck and safe travels!