Originally the World of Warcraft Classic demo (which provides two zones, one for each faction, for levels 15-19) was just going to run for roughly a week's time directly following BlizzCon's opening ceremony, but the timeline has been extended through several days. It's not ending at 10AM PT on November 12.
Community manager Bornakk took to the forums to announce the news: "It’s been awesome seeing all the excitement building around WoW Classic and the play-at-home demo we released as part of the BlizzCon Virtual Ticket. So awesome, in fact, that we’d like to keep the party going for a few more days!"
As a reminder Blizzard will be pushing out its World of Warcraft Classic content in waves. First it'll launch with 1.12, rolling out Molten Core, Onyxia, Dire Maul, Kazzak, Azuregos, Blackwing Lair, BGs, PVP rewards, Zul'Gurub, AQ, Tier 0.5, Silithus content, Green Dragons, Naxxramas and the Scourge Invasion over time. After that it's anyone's guess what happens (staying stagnant? WoW Classic moves into Burning Crusade?).