Of course, the Public Archives of PEI which is located in Charlottetown is the best place to start. If you can't find there what you are looking for, the Archive personnel will inform you of where you should go to continue your research.
PEI is known for ceilidhs. A ceilidh is Celtic for a musical gathering or also known as a kitchen party and they are a ton of fun. Here is a couple of great links for lists of the ceilidhs that may still be happening;
I think September/October is the perfect time of year to visit PEI. The crowds have diminished, the weather is generally pleasant with cooler evenings and there is enough to do to keep anyone occupied.
I hope this helps with your planning.