I have a question relating to installing an EAP245 or similar

My home network is set up as follows:
- NetCommWireless router supplied by my broadband provider. This sits in the garage, as that was the only place free for a cabinet, but the garage is attached to the house and has internal access. The house is all on one level.
- 2 unmanaged switches, one of which has PoE+ capability (DGS-1008P - D-Link 8-Port Gigabit PoE+).
- The house is wired with Cat 6 cabling for computers/TV etc.

- iPads use the WiFi from the router (2.4Ghz and 5Ghz)

In the bedroom part of the house (which is where the garage access is) I can get both 2.4 & 5GHz, but in the rest of the house I can only get 2.4 which means the iPad switches in and out if I move through the house.

I was thinking of turning off the router WiFi and putting in an Access Point (TP-Link EAP 245) to supply the WiFi. 
I would use an Cat 6 ethernet cable with PoE, but can that be plugged into a PoE port on the unmanaged switch, or does it have to be plugged into the router?

Thanks