I tried to get an answer to this question by e-mailing The Friends of Algonquin Park as mention in the comments by pnuts.
The answer I got was that the outfitting services that are in or ner the park usually all close by the Monday of thanksgiving weekend. Which this year is the 10th of October.
Moreover they also replied that the majority of stores only rent canoes and kayaks. So it would be hard to get boats as asked in the original question.
The e-mail in question:
Hi Johan,
The outfitting services that are in or near Algonquin that would rent boats usually close on the Monday of the Thanksgiving weekend.
The majority of them only rent canoes and kayaks.
Reina
Algonquin Park Information