Well, you aren't supposed to launch motorcraft from the beach here - there's a 100 yard no-motor zone and they don't like the idea of fuel and oil spilling.
There's a chance you can make it without being seen, but there's also a good chance you'll be cited.
If there are launches directly to the ocean, I don't know about them. The Coast Guard is your best source of information (305) 535-8701.
As far as launching from an Intracoastal ramp and motoring out, IMHO both Port Everglades and Hillsboro get very choppy and, even if it's like glass when you leave conditions change rapidly with the tide. I do see small craft out there, but they seem a lot larger than 10' (maybe a zodiac is better in chop?).
Sorry to be so discouraging, but if you can make it out you'll be fine. There are nice reefs here between 200 and 1,500 yards off the beach, and we regularly kayak dive them without the least bit of trouble on most days.