powering a 12V 1.0Amp DC fan
I suggest to review the use of AA bateries due to the current of the fan you need.
Based in my experience you can use 4x 18650 lithium-ion batteries that gives you an output of 14.8v. After, connect them to an LM7812 voltage regulator. This regulator need a minimum voltage of 14.5-15v to operate so will work ok.
The output of this voltage regulator you have to connect it to the fan.
You can use to smooth the signal of the voltage regulator 2 caps in parallel of 100nf and 100uf.