Mania's Arcania has been doing some experimenting with tamed pets on the PTR, and she's got a few great tips for all you hunters picking up new pets. First and foremost, apparently any pet you tame, no matter how happy it is or how often its fed, will stick around with you for at least 30 minutes, so if you tame a new pet and don't have food for it, you've got that long to find some. Dismissing a pet or having it die actually stops that timer, too, so if you don't have food and the time is about to run out, you can dismiss the pet, and then recall it when you have food to feed it.
She's also looked at some more technical information on how quickly pet health returns after various kinds of dismissals-- in most cases, it looks like your pet actually comes back with a lower percentage of health, which then ticks back up to full in just a second. Probably won't affect most Hunters, although a few of the situation she goes through sound like battleground PvP to me, and it could be that Hunters there are using their pets so quickly that it might make a difference. More testing is on the way, she says.
But at least the taming schedule will probably help Hunters who end up grabbing a rare spawn as a pet and then realize they don't have the food to feed them. We've got more breathing room than we knew we had.