There is a long series of moving sidwewalks, located lanside, that connects all of the terminals. It is located one level above the departures/ticketing level. Once you have exited the "H" concourse, the elevator is located opposite the end of the Delta ticket counter.

You can also walk on the main level, since you aren't encumbered with lots of luggage, but then you have to make your way through the teeming masses that lend MIA its, ahem "charm"

Bottom line is, you'll need to clear security once you arrive at the threshhold to your designated AA concourse.