Have a read through
http://redis.io/topics/persistence.
TL;DR
You should be able to manually trigger a BDSAVE to generate a fresh rdb file that contains a snapshot of the redis database. If you have RDB persistence already enabled in the config of your current instance you might be able to skip this step. (The file will already be sitting on your existing redis box). You'll then just need to copy that rdb over to the same location on the new redis box, and enable RDB persistence in it's config.
After that when you boot up your second redis instance, it will load in the data from the snapshot as it's initial state. It's basically the same process that lets redis still retain data through a reboot. You're just grabbing the output of the disk persistence rbd file for the old instance, and using it to boot your new instance.
If you're a bit nervous to try this on your production boxes, I'd suggest just downloading and running redis locally (or in a linux vm if you're not natively using linux). Play around with loading in some data with the redis-cli, then dumping the rdb file, and restoring it to another local redis instance. Getting your hands dirty playing with a local redis like this, is probably better than any step by step guide you'll be able to get out of anyone online, and you'll learn a lot in the process. Good luck.