Right, there's no problems there. You don't really need to "extend" the existing WiFi network. You just need to use the ZF7363 to broadcast the same SSID and password as your existing network. At that point, roaming is a client-side decision and your clients will automatically pick the AP they prefer the most at any given time, including your ZF7363.
We tend to associate the term "extending" with wirelessly extending (e.g. SmartMesh, WDS) in cases where ethernet cannot be provided to the AP. In your case, fortunately, that's not the case, so you can simply just log into the ZF7363's web interface, set up a 2.4GHz and 5GHz wireless SSID with the same WPA passphrase as the other AP's on your network, and all should work.
P.S. Monnat Systems' answer is the right one in the case of wirelessly extending/repeating an existing network. That requires every AP to be a Ruckus AP, and all of them have to be managed by a ZoneDirector.