Awesome, I wrote a pretty solid paper on this topic in university.
Before you can use the term feminist, you must first agree on its definition. In the interest of brevity, there are two schools of thought: women are capable of making their own decisions and are free to use whatever tools of empowerment they have to better themselves (traditional feminists), or those that believe that women who engage in activities like prostitution, are perpetuating a culture of male domination through objectification (neo-feminists).
Both sides have valid arguments to their claims, and the issue goes far beyond prostitution. You must also think of advertising, clothing, societal norms of marriage and relationships/courtship, etc, etc...
One of the more interesting arguments I've heard from the feminist perspective postulates that a woman who marries for money is no different than a prostitute, and may in fact, be morally far worse than a prostitute. For the woman who sells her body for a sum is being honest about her intentions, while the woman who marries for the money is lying to her partner. In both cases, money is being exchanged for companionship, but in one instance, a woman is honest, and in the other, the woman is not.
Conversely, neo-feminists have a strong argument that dictates prostitution perpetuates the notion that men are superior to women, and that they can be bought and sold as if they were common property. This is evidenced by the phenomenon of sex-trafficking and abuse. While factual evidence on the numbers of victims of sex-trafficking remains a hotly debated topic, it is a known phenomenon that cannot be ignored.
Lastly, we often forget about males who are involved in prostitution. Is it immoral for them to employ themselves in this profession? Are they abused in the same fashion as women?
It's a truly fascinating debate that I particularly enjoy having.