AA in YUL certainly can you all the way through, and the likelihood of everything going smoothly is extremely good.

However, if you've got lots of time between flights (and it looks like you've got a 4-hour layover), you can reduce the risk of lost baggage by checking your bags only from YUL to JFK, then carrying them yourself to the Qantas terminal. Not really a whole lot of extra aggravation on your part (you have to clear US customs/immigration in Montreal, anyway), and there's certainly not a whole lot to do at/near JFK.