I was working on something like this about 2 years ago and it still works for me for about 6months or so on 2xAA.
Please, check the following github project page
https://github.com/endysh/Wireless-PIR-sensor
With some improvements (I did not have a chance to finish yet) the power consumption in detection mode can be reduced down to 60 - 70 uA, which can give you 1+ year, but it depends on traffic and how often it will send notifications