Poz,
You state you have four users, but you don't state how many computers you are using. From your description, it could be four or more. I am guessing you have three rooms with six computers.
First answer. If you are going to do P2P, then don't use the new computer. Just let it work as a "server." It just depends where you are going to dictate. If the new computer will be in your office, then dictating there would probably be OK.
A question. Do you have two nurses working full time?
The server vs. peer-to-peer debate is a long one and probably occupies 20 threads. Personally, I agree with your IT.
You didn't say much about the computer you have. How old is it? Could you just add more RAM to one of them?