I will agree with sturner that that multiple server brokering is much more complex, but worthwhile in the end. I find the Service Broker tool to be rather robust.

What you want to do here, though, is deactivate the target queue in the database, and move that over to the otherside. Your source queue can build things up for a good long while (just watch it, make sure you don't end up bloated by accident). As long as your source queue is still getting records, and you've got space on the source system to store them, you can take as long as you like setting up the delivery server... Just realize once you bring it online it's going to take a while to process all of that.

A recommendation, however. Setup a testing database between the two servers to pass a simplified queue setup between them to make sure you've got all your endpoints and the like setup properly. Service Broker gets complicated fast with all the moving parts, try to simplify the setup and routing to get a feel for it before you start testing the connections.