If you have herb/eng/mining this is really simple to do and you will make a ton of gold, it just takes time.
Spam this macro while flying from spawn point to spawn point gathering-
Since it isn't a hard 6 hour spawn timer, there is no way to predict when you should go - you just have to get lucky. If you camp it for 6 hours straight you actually have a really good shot of getting the cat b/c her 10 min life span you should hit her spawn point at least twice. You still have to deal with the odds of someone else just happening to be there and taming/killing her, but that's why you use the term rare.
Regardless of if you want the other two pets, kill them to get the spawn timer rolling again.