We did the very same thing for the very same reason in 2007. Immigration is not as well organised nor as pleasant as it is at Orlando International and it took us longer to get through. Compared with Orlando, it seemed to take us forever (although we do have it down to a fine art there), and you won't find your carpeted immigration hall equipped with friendly staff pointing you in the right direction. The hall at MIA is fully-functioning concrete and non-existant help. We felt desperately sorry for the 70-something, non-English speaking lone traveller who was sent to to the back of the line after queuing for 30 minutes. We tried to no avail to get someone "official" to take on her plight. It still troubles me to wonder what happened to her. We were through immigration in around 45 minutes and, although it seemed like a lifetime, we remained chilled, reminding ourselves that we were on holiday

. On top of that, all the car rental companies are offsite, so a shuttle ride is unavoidable. The infrastructure around the airport is a mess, but we'd dropped off a hire car there the year before ahead of a cruise, so we knew what to expect. Despite all that, we were checked in at our Palm Beach Gardens hotel (more about that below), showered and changed, and sitting at the bar by 5.30pm. If we'd needed to drive for another 2 hours, I'm sure it wouldn't have been a problem, but I'm glad we didn't have to.
Our flight landed on time (14.15 EST), but given that we had no guarantees, we'd opted to drive just part way that first day. Having researched a suitable stop-off point, we found a great rate at the PGA National in Palm Beach Gardens. It was the shorter leg of the journey in terms of mileage, but about half way time-wise as getting out of Miami takes a little time. We were awake at the crack of dawn and, even after waiting for the restaurant to open at 7am for a spot of breakfast, we were checking in to Disney's Saratoga Springs before 10am the following morning.
We had NeverLost SatNav included which helped, but I'm sure we would have found our way out of Miami with the map we'd brought with us (especially as we'd driven to MIA the previous year). The worst part of the journey from Miami to Orlando is getting out of Miami, particularly if you have to do it during the rush hour. Luckily, our Virgin flight from the UK landed shortly after 2pm local time (significantly earlier than the two daily flights into Orlando). I'd say you need to allow a good hour and a half to clear immigration, customs and get the shuttle to the car hire depot. From the airport, there are two main routes out of Miami - the Dolphin Expressway east to the I-95, or the Dolphin Expressway west to the Palmetto Expressway. Either way, you want to head for the Florida Turnpike - by far the quickest route to Orlando. The I-95 is the shorter route, but I'd recommend taking the Palmetto Expressway - it's far less busy, particularly during rush-hour. Once you're on the Turnpike, it's an easy drive to Orlando. I'd recommend taking a good look around the Turnpike's website. It's a toll road, but the middle section is a 'ticketed' system which means you travel for a fair distance without having to stop at a toll-booth.
The only real downside is that you spend your last day travelling. Our flight wasn't until 19.25, but we had to leave Orlando at 10am. We drove all the way to Miami, stopping for something to eat at Hollywood (there's a great complex there literally just off the Turnpike at the site of the Hard Rock Casino, which I'd highly recommend). Obviously you have to go through the whole shuttle thing with the car again. We were at the airport in plenty of time, but couldn't risk leaving it any later to leave Orlando in case of hold-ups. MIA isn't the bright clean environment of MCO, but it does have plenty of shops. The eating options aren't very inspiring, so a stop en-route is the way to go. We would do it again if the price was right, but we'd probably tack a day onto the end of the trip.