With a few notable exceptions (including all wild pets), you will be able to access any pet on your account on any realm, put it into a cage, and sell that cage on the auction house. You've just essentially taken money from a character on one realm and put it into the pockets of a character on another realm.
Right now, the only way to move money between realms is to use paid character transfers, and the only way to move money between Horde and Alliance on a realm is the neutral AH. Blizzard has implemented some barriers designed to limit the amount of wealth that can be moved between realms (like limiting the amount of gold you can bring) and has stated that they don't support using the neutral AH as a way to move wealth.
Will this make it to live?
If the ability to use pets this way really was an oversight, it's possible that Blizzard will make some changes. For example, they could allow you to freely use any pet on any of your characters, but only cage and trade pets on the realm they were learned on.
Personally, I hope that they don't do this. I think the ability to send gold across faction and realm boundaries is not actually bad for the game. It allows friends who play with each other from multiple realms through Real ID BGs, dungeons, and raids to gift gold or pets to each other, just as if they were on the same realm. I do understand not allowing players to mail gold between realms: while I can't precisely predict what effects this would have, I imagine it would make the economy even less useful for an average player on an average realm.
That said, moving pets is different than moving gold. When you use pets, the total amount of gold in each economy doesn't actually change. The only way to get the money on your target character is to sell the pet on whatever realm you're sending the money to, which comes from another player on that realm. Also, you're going to have to compete with all the other pet sellers on that realm to get your money. This means that if one realm is a really popular target for gold transfers (like a big PvP realm might be), the amount of gold a pet will sell for will go down as more people try to move money there. This push-back will have a natural limiting force on the amount of money "moved."
So even though pets are traveling from one realm's AH to another, no actual gold is moving. Every time someone uses a pet to transfer wealth, it's a zero-sum activity for the economy, somewhat similar to buying a Guardian Cub or a loot card and putting it on the AH. It doesn't contribute to gold inflation at all.
We may have to start worrying about pet inflation or deflation on certain realms if people moving money aren't adequately balanced by others moving in the opposite direction, but that's a self-solving problem. If pets become scarce on a realm, someone will see an opportunity to make money by bringing pets in from realms where they're abundant.
What can I use this for?
The benefit for players is pretty big. As I mentioned before, you'll be able to help friends out on other servers and factions than the one where you have your money. Also, if you actively play on two servers/factions, you won't have to pay real money or bend over backwards to boost your alts with resources from your main.
If you happen to be in the business of making gold, this presents an interesting brokerage opportunity. If there's a discrepancy between the price of pets on two realms, you can make profit by moving pets back and forth. For example, if my home realm, a medium-population PvE server, has high prices on trained pets, I could transfer one of those expensive pets to a realm where the average pet price is lower, sell it, and use that money to buy a bunch of cheap pets to send back to sell on my home realm for a profit. Of course, this would only work if the loss I take on the initial pet is compensated by the profit I make on the return pets.
Alternatively, if you play on a realm where pets are cheap, you could buy them up, move them to realms with a high average pet price, and use your profits on the other realms to buy pets that you can sell on your home realm. Again, you need to remember that you might lose money when you bring your money back home.
Maximize your profits with advice from Gold Capped. Want to know the very best ways to earn 10,000 gold? Top gold making strategies for auctioneers? How about how to reach 1 million gold -- or how one player got there and then gave it all away? Fox and Basil are taking your questions at firstname.lastname@example.org and email@example.com.