AppleTV HD apps work over ethernet but not wifi

I'm about to take the device into Apple to see if they can replace it for me - its only 6 months old.

They could replace it, or test it, but if the issue is your home network, then a replacement set-top box will have the same issues as the current one.

Describe your home network. One device as modem/router/wireless access point, or more network regulating devices?

Did you try restarting the router (and optional other network equipment)? Re-initiating the connection might solve some issues, without making actual changes.

Signal strength is not the issue, in my opinion, when Home Sharing with video works over Wi-Fi. It can have similar bandwidth demands on the network as apps would have.

Run Speedtest on the Apple TV to know the bandwidth available to that device. A weak Wi-Fi signal or signal with interference will show a much lower speed than normally expected.

Run iStumbler the room the Apple TV is in and you will likely see your Wi-Fi signal is not strong enough to stream. Depending on the amount of Wi-Fi devices you have and the size of your home you may be a candidate for a Mesh network.