The patch 6.1 PTR realms are now live, but without any level 100 characters there isn't much to test yet. All PTR realms are still locked to Mists of Pandaria and there is currently no ETA for when they'll be upgraded to Warlords of Draenor. Character copy is disabled, but you can make pre-made level 90 toons.
One of the few things available for testing is the new heirloom interface. Once you own a heirloom, it's a simple matter of clicking it in your heirloom tab to create a copy of the item in your bags. You can buy heirlooms and upgrade tokens from Estelle Gendry (Undercity) and Krom Stoutarm (Ironforge). Base level heirlooms scale from 1-60 and can be upgraded twice to level 85 and level 100. See here for a full list of the heirlooms available.
For more details on the status of the PTR realms, check the blue post after the break.