We did it almost a decade ago. We flew into Sanford/Orlando airport, got on a route that took us to 95. Took that south. North of Miami, we switched over to the turnpike and took that South to Homestead. IIRC, we then got on Route 1 South. Once you get onto the keys, you turn left to go to Key Largo while traffic heading to Key West turns right. I vaguely remember a road called the Sawgrass Expressway and using that to avoid more heavily traveled roads around Miami. If you have a map available, check that out.
I would think traveling from MCO, you would want to take the turnpike south. There's no need to go out to 95. We traveled at night and made it from Sanford to Cudjoe Key in about 6 hours, when we were told to expect 8. Considering Key West is about 3 hours from Miami, I would guess you can get to Key Largo in about 5 hours.
HTH! Have a great trip!