The ER-X set up as you described should work for you. I have heard some people say that the PoE injector may not be able to keep up if you have a lot of wireless clients, but I doubt that will be an issue in your case.
If you do run into those issues down the road, you can just replace your PoE injector with a (cheap) 24V 1+A power adapter for the ER-X. With a 24V power adapter, the ER-X is able to pass through PoE without the PoE injector, and 24V 1A is more than enough to power both devices.
If you do run into those issues down the road, you can just replace your PoE injector with a (cheap) 24V 1+A power adapter for the ER-X. With a 24V power adapter, the ER-X is able to pass through PoE without the PoE injector, and 24V 1A is more than enough to power both devices.