There is AVE service now, so I don't see any reason why it wouldn't be available in October. Depending on what time you want to leave, you many need to change trains, apparently at Antequera.
You won't be able to see the October schedule for quite some time, but go to Renfe.com and check the schedule for next week for the day you plan to travel, using Barcelona-Sants as your destination:
I looked at a couple of weekdays and found a 7:10 AM departure (connecting in Antequera) and a 3:45 PM direct train that doesn't require a connection. The afternoon departure gets you to Barcelona at 10 PM.
Those same departures are on the schedule through April. It appears that if you monitor the Renfe website (probably not necessary until late May or early June) and buy your tickets when they first go on sale, you'll be able to get the afternoon train for no more than 60 euros. The early-morning train may cost more like 82 euros.
Renfe's website is a bit odd about connections. It appears that you could leave Granada later in the morning or early in the afternoon, spend a bit longer on the train, but arrive substantially earlier than 10 PM. If the prospect of a 7:10 AM departure doesn't please you, you probably have two later options. The late-morning train requires three connections, which would be annoying (and possibly stressful if you have much luggage); the early-afternoon train has only one connection, in Antequera. However, if you had to buy separate tickets for the two legs of the early-afternoon train because they are not coupled on Renfe's website. I don't know what would happen if the first train was late, causing you to miss the second one.
You can take a look at the connections Renfe isn't publicizing on the Deutsche Bahn website.