looking for a job for the fall

I’m on the lookout for a new job to start in the fall so I can save up for my next semester and the subsequent ones. I make really good money where I work now and want to stay there as long as I can. When is the best time to start looking? I’m thinking after 4th of July weekend would be good because it wouldn’t be long before all of the people who have summer jobs would be quitting.