Adding a new domain to an existing tree

My company network consist of only 1 domain (Windows 2000 Platform), as mycompany.net.eg.
The Virtual internal subnet that I am using is 192.168.10.192-255 with a subnet mask 192.168.10.192 (nearly fully used). Now I have to create additional domain. I am thinking of creating a child domain (as NewDomain.Mycompany.net.eg). I started to plan for it, but I found that I am in a dilema.
Do I have to specify a new subnet, a new DNS and DHCP or use the exsisting ones and use a DHCP relay agent. Please tell me what is the plan that I will follow and the tricks that I may find.
I can give the whole 500 points to the answer that will fulfill my needs.