In general, it's best to avoid the busy season for moving companies, which is often in the summer months when school is out, and families are relocating. It's not impossible to get the moving date you want during this time, but you'll need to book your move many months in advance.  Keep in mind that summers are very hot in Miami—if you're planning on a do-it-yourself move, you may want to wait for cooler weather if you can.