Let's look at the facts for this:

Quina can wear Tiaras. Only female characters can do this.

On the flip side

Lamia's confusion spell, I'm pretty sure, only affects males, as it's a type of seduction thing. I have had Quina be affected by it.

there are several times when they refer to Quina as a him or he instead of s/he.

According to previous posters, Quina has been Covered by Zidane.

So obviously the answer is confusing, it would be easy to just assume it has no gender, although Qu's should have gender as Vivi referred to Quan as Grandpa, not Grandma or grandp/ma...

One interesting note is that Gogo in FFVI was referred to as the same way, its sex was unknown.