Nope, you can't just plug and go, unfortunately. You'll first have to get your tunes onto the mac, and then have your iPod sync with the new computer.
So, when you plug it in the first time, and it says that your iPod is paired with another computer and asks if you'd like to pair it with this one, click "no." You can get your tunes off the iPod any number of ways...I use Senuti. (do a search for it...) It's a great program that shows me what's already been downloaded and put into itunes, as well as shows me playlists. I haven't ever tried downloading a playlist, but I imagine you could just click on it and hit the down arrow...I'm not sure though.
If you want to keep playcounts and all that good stuff, you'll have to find the two files that iTunes uses to keep track of everything. One is an xml file storing song data, and the other one (I think) stores playlist information and all that good stuff. There was a topic on these forums I read today about which two files those are...it was called something like, "what do the 2 iTunes files do?" or something like that.
Once you have all the music on your new Mac (congrats by the way), then you can pair your iPod with the computer.