That stucco is pretty thick.
Most newer house in FL are built with concrete block. And most of the time, the "cell" of block where the hose bib is will not be poured full of concrete. So, if the waterpipe in your house is copper, you can often chisel the stucco away from the hosebib, pull the hosebib away from the block, and cut the old hosebib off with a hacksaw. Heat the sweat collar of the old hosebib up and pull it off. Sweat a new male adaptor on, use lots of teflon tape (10 wraps) and some pipe dope, and CAREFULLY thread a new bib on. Do NOT overtighten it, as it is easy to twist the copper pipe. Push the bib back into the wall partway, and use some sand mix to patch the stucco.
If, however, your home is not block, or is piped in CPVC or PEX, you would be most wise to leave this one for a proffessional. And if you don't feel comfortable pulling on your waterlines, or sweating copper, you would likewise be ahead calling a plumber.