It's female, because it's a nidoqueen ...

Yyyyyeah, on this site? With the "tag what you see" rule, and especially with the herm and even male Nidoqueen images that have been posted? Sorry, Danjen, but that doesn't mean anything. Tags changed.

It's shape is feminine, it's species is by default ONLY female, and it has pronounced eyelashes, a feature generally reserved only for females. Seriously, if you need a vag shoved up your nose to be able to distinguish one gender from another, you need to get the porn sites and get out in the real world so you can become familiar with the more subtle indications of gender.

Removed the dinosaur tag, as no one in either of the "Nido-" evolutionary trees are referred to as dinosaurs. Nidoqueen is known as the "drill Pokemon", as is Nidoking. Nidorina and Nidorino are the "poison pin Pokemon", as are both genders of Nidoran.
Bulbapedia speculation is that "Nidoran♀ appears to be based on a porcupine, rabbit, mouse, hamster, or some combination thereof", and while Bulbapedia doesn't have final say with these things, considering Nintendo nor Gamefreak have specified the animal they're based off of, I feel that Bulbapedia sets a good general guideline for these kinds of things.

I also feel that, since Nidoqueen doesn't come from a fossil, it's safe to assume it isn't a dinosaur.

Just enjoy the Nidobooty already x3