I'm fairly sure that was all cosmetic changes to his head. And no actual gender changing.

not only did they reduce his lobes (lobes being an erogenous zone on a ferengi)

he also was given breasts, adopts a more feminine voice pattern, ect

Quark/Lumba even attempts to prove herself a female by exposing her assets to the other ferengi,

Brunt still exclaims that Quark/Lumba is a male.

and what does Nilva say? "Shes close enough for me" and the key word is starting with SHE, she was a female for him, no matter anything else at that moment he is staring at a female ferengi named Lumba.

I argue that in this point Quarks precieved gender changes from male to female, and perception is what makes a person who they are. Quark becomes a female.