Maemo Mapper provides the ability to search for POI in your area, and from that you can download a route to whichever POI you choose. It may not be a single click, but it's not more than a few. There's also a DBUS interface for Maemo Mapper, which doesn't have a "send address" function yet, but will soon.

But how to send the address information from the browser to Maemo Mapper is the real problem. djs_tx's suggestion (a network daemon listening for certain network traffic patterns) may sound straightforward, but the kinds of patterns to look for are likely complex and non-constant. Roger's idea is likely impossible without access to the browser's source code.