Lots of day trips you can do while your here and your here for quite a while so I am also going to suggest going to the mainland at least overnight if not longer if possible.
Some suggestions include
Lamanai mayan Temple and Jungle river trip
Manatee watching trip with beach cookout
Tubing on the river through the underground caves on the mainland.
Also if you can spend a few days on the mainland visiting the cayo district swimming in the mountain pools, canoeing down the jungle river (one of my favorites.
These are just a few suggestions not sure about the deserted beach thing have not heard about it but then again if I had it would not be a deserted beach I SUPPOSE :-)
Playa Blanca Beach Resort www.playablancabelize.com