No. Just no. That is Unwizardly, not to mention this is Wizard101 not Fight101. I don't ever see how this could work in the Game. This is a Family Game. You can't put in violent stuff cause there are Kids in the Game. (And that would put a bad influence on MOST Kids) I don't even think Adults or Teenagers would find pleasure in their Pets beating up another Pet.
If you have the urge to see some Wrestling, you can go watch Wrestling on the TV. You can go play Violent MMOGs & MMORPGs with Wrestling. No-one is stopping you. :)