Renting is not easy, certainly not if you plan on flying yourself. Most rentals are from aeroclubes where they are used for training, so they are very reluctant to rent them out for more than an hour or two, and for local flying only.
You will normally need to convert your PPL (EASA is probably easiest) which will involve a written test and a check ride at the nearest aeroclube, and then sending your papers of to ANAC. Depending on the aeroclube they might be willing to let you fly as soon as the process is underway, others might insist that the documents come back first.
The best idea would be to get in touch with the aeroclube nearest to your planned destination and ask them about it. I've always found these people to be very helpful and polite, but frankly I doubt that you will have much success, and I certainly wouldn't plan on using it as a means of transport. Unless you have a lot of hours very few places are going to let you fly off into the sunset without having at least the value of the aircraft left on the table.
Hope that helps