Thanks for the picture 
Glad you got it working!
For a Fob (3V battery), I just use a switch to power the device. In your case (~4.5V battery) you can use a P-Ch Mosfet for power and switched with an N-Ch Mosfet for switching the power.
A simple circuit is below.
Switch turns on the power, Hold (GPIO) keeps it turned on until no longer required.