IMO, this is doable, but cutting it close. I'd rather not do this with checked bags and without PreCheck.
Bag delivery times for AA in MIA aren't the fastest. Expect at least 20 minutes, more like 30, from deplaning until you can leave baggage claim with your bags.
Minimum check-in time for Delta in MIA is 45 mins. with or without bags. No idea how strictly this is enforced and if you can do OLCI for the HAV flights.
The AA flight your QF one is a codeshare on usually lands at the E satellite gates which is a train ride or long walk (I'd say about 1.2 km) away from the H gates in the South Terminal where your DL flight will depart.
Miami airport is a zoo more often than not. Security wait times especially on the standard lanes (assuming you don't have PreCheck) can be maddening.

If worst comes to worst and you miss your flight, you'll have to overnight in MIA as the DL flight you booked is the last one of the day going to HAV on any airline. Check hotel pricing... can be very high. I got stuck there once and had to shell out more than $200 for a rather mediocre motel...