Can I install my paid license of avast on the new Laptop?
Or do I have to buy another?
It depends, how many licenses did you buy…?
Or if you have 1 license, for how many systems is it valid ?
OK it says:
Product Name: Avast Internet Security - 1 PC, 1 Year.
So can I disable it on the old laptop, and enable it on the new one?
Yes, that is possible.
- Remove avast from the old system
- Remove the old system from your account
- Install avast on the new system
- Use your license file
- Connect the new system to your account
To remove it from your account, go to my.avast.com
Select the device > click on settings and then select “Delete from account”
Of course you can always use Avast Free on the old laptop 
Greetz, Red.