Certainly can be done. Lets say you get out at 7:10am and you want to be back at 11:00am that gives you almost 4 hours. Plenty of time but probably not worth it especially since getting to Miami Beach takes times. If you really want to get out of the airport get on the metrorail connect at government center to the metromover and go find a place to eat in the Brickell neighborhood. Not sure what places will be open at 8:30ish though.

But IMO I would just stay in MIA. Plenty of decent food options in the North Terminal.