Honestly, why would you want to do that? Obviously, you're talking about booking separate tickets on two different airlines, which can be a real recipe for disaster. If you miss your first flight or your first flight is late, then you will be viewed as a NO SHOW on your second flight. This means that the airline has ZERO obligation to you, to get to your final destination. I have to assume it's cheaper, but to ME, no way it's worth it.

Sort of addressing the question, I personally would not do anything less than overnight. If you're just driving without stopping, with NO traffic, it takes approximately 35 minutes. Add in traffic, who knows?? Add in, deplaning from your first flight, getting all the way outside, getting a taxi, travel time to Miami, and then you have to go through TSA in Miami. WAAAY too much possible drama for me, for anything less than an overnight situation.