If this is the case, what would we need to do in order to install VoIP onto our system?
If your switches have a software load that supports quality of service you will have no problems. If not, a simple software upgrade will fix you right up. The fiber will have nothing to do with it. A packet is a packet and will travel anything that supports IP.
I really don't understand this comment. I am looking forward to your response. My guess is that your communications company is used to dealing with much smaller networks that don't have fiber -- for instance, very small local area networks that are all copper attached. Can you please also let me know what phones you are considering? I look forward to hearing from you and thanks!