'Search Domains:' box is blank on all client Macs

Hello all,

Could someone please tell me whether it's normal for the 'Search Domains:' box (System Preferences > Network > Airport > Advanced... > DNS) to be empty on all of my client Macs that are connecting locally to a DNS server (Mac Mini running OS X Server 10.6.3) on a LAN configured thus: -

Server (Mac Mini running OS X Server 10.6.3, hosting AFP, DNS, OD, SMB & VPN)
Manual IP: 10.0.0.254
Subnet: 255.255.255.0
Router: 10.0.0.1
DNS Servers: 10.0.0.254
Search Domains: mydomain.co.uk

Router (acting as the sole DHCP server)
LAN IP: 10.0.0.1
LAN Subnet: 255.255.255.0
DNS Servers: 10.0.0.254

Wireless access point (Apple Airport Extreme Base Station)
Manual IP: 10.0.0.11
Subnet: 255.255.255.0
Router: 10.0.0.1
DNS Servers: 10.0.0.254
Domain Name: mydomain.co.uk

Client machines (all Apple MacBook Pro laptops running OS X 10.6.3, connecting via Airport, using DHCP)
DNS Servers: 10.0.0.254 (auto-populated in grey)

Everything else works perfectly, however I would like the ability to type a short local URL - e.g. router, rather than router.mydomain.co.uk - at client level as well as server level (obviously with the server having a manually inputted search domain, the short URLs work within it's own web browser, but not at client level).

Is there a way to fix this? Am I missing something simple? Any help would be greatly appreciated.

Many thanks.

Dan.