I'm going to assume you're asking this because you used your older version to upgrade to the new version. With most software companies doing so invalidates your older license. Sony is very different, and very nice in this respect. Your old license remains valid and you now have an additional license. The only difference between buying a new version outright and doing the upgrade is that you get a discount on the new purchase. I don't know of any other company that does this. So yes, you are welcome to install on the new laptop.
Your license also allows you to install Vegas on multiple computers that you own, as long as you only use it on one. So, if you want to you can install 13 on your new laptop as well. This has the advantage in that you can share .vf project files back and forth between the two PCs. If you install the older version then you can open .vf files created on the old version in the new one, but not vice versa.