Yeah, that's not tall enough.
Go to Lowes or Home Depot, and buy a chainlink fence CORNER post. That's 2-3/8", and perfect for this. You can buy one in various lengths. Even in Florida, I'd bury it at least 3' deep (possible wind load makes this SOP), then 5' minimum height. So, an 8 footer should do fine.
Personally, I'd use a minimum of 3 - 80lb bags of Quikcrete in your hole. Bell out the bottom a little bit, and lay a (leveled) patio paver in the center of the hole for the pole to rest on. Might not be needed since this isn't a BUD, but it can't hurt. That helps keeping it from sinking deeper, if your soil is loose. Also drill a hole through the pole about 1' up, and stick a bolt through it. Once the cement hardens, that keeps the pole from possibly spinning inside the cement.
Trust me, it's MUCH cheaper to go what might seem a bit overboard on the foundation of your dish, than to need to have to go back later and do it all over again properly. Besides, Quikrete is cheap. My 7.5' C-band dish has 980lbs of cement in a 4' hole. Then again, we have heavy winds, and softer sandy loam soil.