There actually two Queens
Nemesis and Mothra
The only two female Kaiju that qualify.
Also the only two worthy mates for the King.
Media: Mothra have her own movies.
Nemesis have a whole book series and a comic of her first book devoted to her by Jeremy Robinson.
Now these two are equals to each other both strong, fast and powerful. They would (in Nemesis case) and give (in Mothra case) the king a run for his money. Now I know what you are saying Mothra is not a destroyer She is a good guy. Don't like it then I can take her off this list.
And both have Queen of the Monsters on their titles.
Mothra Powers: flying, shooting beams, speed, healing pollen, can make big gusts of wind with wings.
Mothra Weakness: when hit take damage easy because not heavy armored.
Nemesis Powers: Speed, heavy armor, orange membranes that when punctured cause a huge explosion depending on how much of the orange liquid is exposed. She can shoot a glob of the orange liquid from her mouth as a long range attack. Sharp claws, teeth and tale. And in her white form have wings that can reflect light into a beam that can cut anything.
Nemesis weakness: sharp objects like claws or big blades can go into her armor, her white form has no armor So is very vulnerable to attack.
Queen Powers: one of the most powerful pieces of the game can go anywhere.
Side note: Nemesis is my favorite Kaiju, when I read her book that what got me back into Kaiju the first one being Zilla.
For Mothra same thing as for Gamera I just know about her a little more actually a lot more than Gamera and can't wait to see her in Godzilla 2