I just started with Macs too, but I've done a fair bit of DNS. You're proposing a DNS server that faces two ways, and for a small network it really isn't worth the pain. It involves quite a bit of mucking with config files. I just took a look at the interface for DNS in Server Admin and they don't even provide the possibility of doing this, as far as I can tell.
But there is a relatively easy solution!
Add example.com to the hosts files on all of the PCs behind the router. On OSX this is /private/etc/hosts on windows machines it's aproximately c:\windows\system32\drivers\etc . Searching is probably best. You'll need to add a line
www.example.com 192.168.1.1
I hope that helps!