You will get a 1G refurb, Apple doesn't give 'upgrades' for broken iPods.
I've dealt with Apple regarding iPod replacements no less than three times (string of bad luck, unfortunately), and I always got one of the same model and generation in return. For example, the first iPod I had that became faulty was a 5.5G 30GB iPod classic; this happened well after the 6G came out and the 5.5G ceased to be available, but I still got a refurb 5.5G in return.
Apple Stores also tend to have old model refurbs on site, and considering the 1G iPod touch was only a year ago they would probably still have refurb models out the back.