If you want to fly direct, you'll need to take Northwest. Sun Country has seasonal service, but the season ends Saturday. There are three MIA-MSP flights a day on NW. Flight 570 leaves at 7.25 on an A320. Flight 574 leaves at 13.05, also on an A320. Flight 999 leaves at 8.10, but has a stopover at DTW which will almost double your total time until arrival. On Mo-Sa, this flight is on an A320, though on Su, the MSP-DTW leg is on a 757. However, my suggestion would be to take United. Take flight 1814 (MSP-ORD; 16.00) and then connect at ORD on flight 997, which is operated by a brand-spanking new international 777-200 (leaves ORD at 18.09. Approx. 45 minute layover).