Why did Godzilla not kill the Muto Queen?

Godzilla was tired from his fight with Ghidorah so he wasn't in the mood to start any other fights. The MUTO Queen saw what Godzilla did to Ghidorah and probably knew that he would kill her if she tried to challenge him, so she backed down and submitted to him. It's possible that, due to their natural rivalry, they did eventually fight each other, but during the moment they called a temporary truce.

I got the impression Goji was ready to fight at them all but they bowed so he didnt.

HinikunaGoji

Might have been a little of both. He was probably tired from his fight with Ghidorah and probably didn't want to get into any other fights at the moment, but was still willing to fight if he had to. The look he gave Rodan in that scene seemed like an "I'm not in the mood for your crap" kind of look, and the look he gave to the other titans afterwards seemed like an "anyone else want test my patience?" look. At least that was my interpretation.

Gojira Forces (Lim Chen Xi)

Thank You :)

Nice, that clears up a lot for me thanks!

But I would like to see that fight if it happened, and if not he should have killed her.