What should I do about a cat polymorphed into an invisible monster in Nethack?

I am a lawful human Valkyrie that crawled down the dungeon to the Oracle with a cat and a dog. The problem is that my cat accidentally stepped on a polymorph trap and he turned into an invisible monster. I do not have related intrinsics or extrinsics and I cannot see him, nor do I know what kind of monster he is now.

What is the best way to cope with such a pet?

Solution 1:

Since the polymorph trap doesn't disappear until you step on it, just push your pet onto the trap again (after letting it heal up so it doesn't die of systemic shock). it should turn into some other, ideally non-invisible monster.

If the polymorph trap is gone there are usually some in the lowest levels of the Gnomish Mines.