Yes, you are going to hit some of the Miami rush hour traffic, and probably some Ft Lauderdale traffic.
The Turnpike is under construction from a little north of Homestead past Kendall, a distance of probably 15 miles, and you will get significant congestion there. That will be the slowest part of your entire trip, but it will start to get better once you pass Kendall Drive (SW 88 Street)
Once you get north of Bird Road (SW 40 Street) the construction stops and traffic will open up. A little north of Bird Rd, FL 836 (Dolphin Expressway) will branch off to the East toward downtown, and much of the traffic will go east and you will then be going against rush hour traffic.
The Turnpike will eventually turn east, and once it does, you have two choices. One route is to continue east on the Turnpike, it will turn north again, and just stay on it to Orlando.
The other route is to take I-75 North from the turnpike to remain way out west as you go past Ft. Lauderdale. That route takes you north to the big interchange with I-595, I-75, and FL 869 (Sawgrass Expressway). In that interchange, you stay in the middle lanes and go north on FL 869 until it turns east and takes you back to the Turnpike.
Sometimes the I-75/869 route will save you a little time. I just checked it right now (which is about the time you'll be in this area) and Google Maps routes me this way, saving 8 minutes.
Just use Google Maps and take whichever route it recommends at the time you come through.
You will also get some traffic on the Turnpike between Boca Raton and West Palm Beach, but that traffic is usually not bad.
All in all, it's not a bad drive except for the construction between Homestead and Kendall.