Well I hope that label rumour doesn't come true. I want her signed to a major label.
I'm not sure she mentioned a specific time period in 2014, just that it would be coming next year. Realistically, a single should be premiering very early next year if the album is going ahead next year.
I agree with Patrick that it will take a long time for any single to take off if at all. Some singles take at least 4/5 months and that's with an ideal promo schedule. So if she started with the single in February, that would take her up to July/August time for it to take off. Most successful albums in the US are paired with at least one big song. Alex needs to make that happen or any album would flop.