Looks like it is legal just don't know if he has to have a hunting license or not to kill them if they are on his property.
Dec. 1 – March 1 by all legal rifles, shotguns, muzzleloaders, crossbows, bows and pistols
Those with a hunting license may possess no more than 1 bobcat and 1 otter pelt between April 1 and Nov. 30, 2011, unless pelt has FWC tag. Also, otter and bobcat pelts may not be taken out of Florida unless tagged. Bobcats may be chased with dogs year round.
bobcat: No limit