If you are using hub switches and not hub repeaters you can get away without QoS with a small application as you have.
You have two choices
Extend your existing PBX by linking to a VoIP Router via T1/E1.
(think of it as a second PBX)
OR
Change everything to VoIP.
Specific setups depend on your configuration, (e.g. dialing plan trunking) I recommend you write a small RFP and Hire someone to install it for you.