I don't believe this is a feature of the router. Seems like what you'd need is to also be running a DNS on the laptop, and set the laptop IP as the DNS in the router settings.
I don't know if this is even possible, though I suspect it is.
This looks like something that is possible with custom dd-wrt firmware through DNSMasq, but dd-wrt for the DIR-605L was "work-in-progress" last I checked.
Also, that way you'd be using a custom TLD, like "cedkeswebsite.local"