Most Paladins will go questing after evil and being a prostitute would for the most part interfere with this. However, I don't think a Paladin *MUST* quest after evil. I see nothing inherently wrong with a Paladin that acts as the defender of a town or something--if there's nobody else that can take up the burden and the defense is needed then it's the only right thing to do. Thus you have a Paladin who stays put and needs a source of income.
Lets see what the Paladin can do to make money:
Err...if the Paladin is the town's only defense, why can't they just pay him/her for their services? In a situation like that, it would be a little odd for the town defender to have to turn tricks to feed themselves...what kind of town is this? Any village that would let it's only staunch defender starve in the streets isn't worthy of a Paladin's services. And on a more practical note...what about response time? It takes time to don armor, and if you're attacked while your Paladin is giving a naked rubdown to a client, you could be in trouble. Sound the alarm and hope that the sounds of passion aren't drowning it out, then wait for them to get dressed, find their weapon, and ride out to meet your attackers. Doesn't sound all that practical to me.
While a Paladin's sexual practices are going to vary based on their deity, by definition most Adventurers would make terrible prostitutes; the two lifestyles aren't all that compatible. Successful prostitutes work with return business a lot, while adventurers are almost always travelling. I suppose a Bard or Rogue could turn a few tricks on the road for extra cash, but that's about the equivalent of any Adventurer's "profession" check to find some temp work in their field.