There are several places to rent a car from on property or near WDW. There is the car care center (you can arrange for a shuttle to take you there) or the counter at the Dolphin. There are also several car rental companies with desks at the various hotels in Hotel Plaza.
For the Dolphin, there are several options, but none are direct. For example,
1. You can take a bus to DHS and then the boat to Dolphin
2. Take a bus to Epcot, walk through the park to IG, and then a boat to Dolphin
3. Go to DTD and take a bus to the Dolphin.
For the car care center, I think you can arrange to have a shuttle pick you up and drop you back at POFQ.
The easiest route (to get anywhere) is to take a taxi, but that will cost around $15 (my guess).
The Dolphin and Car Care Center have
Alamo/National desks. I think the Hotel Plaza has other options.