You do know that push notifications are actually sent by google servers, don't you? so unless you register your app for push notification with google, you can't use their push service.
Alternatively, you can re-invent the wheel and write up your own service for push notification which will be installed separately and as a background service on Android device. This service would run all the time even when device screen is off or locked and register itself to your own push server and maintain a constant contact with it even when device's network switches from wifi to cellular data and vice versa. This push server will then be used to relay whatever you want to push to android app through your push service running on that android from kamailio.
Developing such a service is beyond the scope of kamailio, so i suggest you better contact Android dev forums for this.
Thank you.