We always fly to Miami too so have done the drive often.
The drive is fine, except the traffic can be very busy in the Miami area on the interstates/turnpikes, so if you get stressed with busy traffic it's worth bearing in mind.
I'm not sure I'd recommend a mini-trip from Orlando to Miami specifically - as others have suggested a bit further up the coast might be more relaxing.
A quick traffic avoiding tip for MIA airport - last time heading back down the Fl Turnpike we kept on the Turnpike looping west instead of taking the I95, and then took the 836 east. It was slightly further but we have had stressful journeys back to the airport while getting stuck down the I95.