What pets?

I'm pretty sure last years coins disappear when the event starts....

I'm pretty sure the Coins of Ancestry stick around, since they do not have a duration. I still have my stash from 2010.

The new pets referenced:
Lunar Lantern: http://www.wowhead.com/item=74610
Festival Lantern: http://www.wowhead.com/item=74611

It remains to be seen if these are faction-specific. In any case, they are NOT BoP (at least according to wowhead), so if they do wind up being faction-specific, it may be possible to get it on your Horde toon and transfer it via neutral AH to your Alliance toon and vice-versa. Here's hoping!

They don't disapear, I actually have coins from two years ago in my bank still.

The pets are faction specific and BOP, so no cross-faction trading on this one :(

Wait, my bad, they're BOE. So I guess we CAN get both, assuming people have enough extra coins left over to buy a second one and auction it.

The Lanterns are definitely BoE; my realm has Festival Lanterns on the Alliance and neutral Auction Houses right now for 10K - 30K gold. If you want both Lanterns, you'll need to spend a lot of money or devise a ridiculously circuitous plan to get it from an alt.