We live in AZ, have a 12 month lease on our apartment. It's up Nov 15, we plan to move but now they say we haven't given the required 2 months notice--is that possible?

You have to read your lease. It may say that you are required to give the landlord 60 days written notice if you don't intend to renew your lease. If that's the case you can give them the notice now and you will be responsible for rent for an additional 2 months.

However you should look closely at the lease. It is possible that your lease contains an automatic renewal. In that case if you don't give them the notice at least 60 days before the lease ends then your lease is automatically renewed for another year.

I gather you didn't read your lease carefully before deciding to move. So now you better read it, because if it has clauses like Lisa mentioned you could be on the hook for another year.

No they cannot stop you from moving out. However, they can hold you responsible for 2 months of rent from the time you give notice. Maybe more.