Minimum battery capacity
The charge of a battery is not from 0V to xV, it depends on the chemistry of the battery, for example, a 3.7V LiIon battery will be 100% at 4.2V and 0% at 3.3V, so you assumption about being 50% of charge at 4.5V is not correct. 

For your calculation you should just use:

Ah=(Wh*tHours)/(BatteryVoltage)

This will give you around 730mAh, then you must calculate the efficiency of your DC DC converter for an input of 9V to an output of 2.5V. 

RealAh=Ah/Efficiency 

Another thing to get in mind is that for such a great time the battery might self discharge, so you should know it's self discharging rate and add it into your Ah calculation.