The big problem here will be measuring a 1 year period accurately without the use of an RTC (real time clock) module.
You can buy little DS3231 RTC modules that have a CR2032 time/date backup battery that should last a few years. Another option would be to use a Wifi enabled MCU that can get NTP time but Wifi is power hungry and not necessarily available.
For the MCU you might consider something like the nRF51822 or nRF52832 as they are very low power standby and can potentially work on a CR2025 for > 1 year but they are not so easy to setup and program in the Arduino IDE.