Landlord trying to backdate rent increase?

She is indeed legally allowed to ask for a maximum of three months back payment on the index-based rent increase. This is very common.
In fact, if you have lived in the apartment for 2,5 years, she is a bit late with this request and you have gained some money here. She would have been allowed to raise the rent on the two-year anniversary of the lease, so in September 2011. As she has only done it now, and can now only ask for the rent increase for the last three months, you don't have to pay it for September and October.