If your pet's health gets too low or its attacks aren't very effective against a certain combatant, you can always switch out your current pet with another companion on your team. Only pets that are considered active (i.e., those in your three Battle Pet Slots), may be switched in and out during the battle. Once the match is over, you can always change up your active pet team, which is useful if one of your pets is low on health or dead.
Apparently a lot of the current World of Warcraft Classic closed beta testers are reporting things as bug that, well, simply aren't. There are enough of them, in fact, that Kalvax, the Classic community manager, posted a lengthy "Not a Bug" list on the forums. Some of the things that are actual features in the game include Tauren melee reach and hitboxes are larger than other races, Warrior health regen is working as intended and creature respawn rates are "much slower".
You are right here. The Rematch string is part of the Info box, and as such it should be parsed correctly. (The string that contains the correct and breed/damage-specific min health requirements). This should be enough, but, I think there are also folks that aren’t using Rematch. They also should know of the type-specific min health requirements. Unfortunatly the default forms of the page don’t offer any detailed entries for the min health. They only offer one entry (for all damage types), and I always put the worst-case min health there (for pets that are weak against the expected damage type)