Is Norton 360 premier edition compatible with a net book?

Can it be installed on a net book?

Yes, although I wouldn't recommend a security suite application like this for a netbook.
You are better off with a more lightweight solution such as a Cloud based idea.
The first free cloud antivirus against viruses - CLOUD ANTIVIRUS (http://www.cloudantivirus.com/en/) is well worth a look and it's FREE.

It would slow the netbook's pitiful little processor as to make the computer almost unusable.

I recommend Microsoft's offering: http://www.microsoft.com/security/pc-security/mse.aspx