Domain mapping for primary domain

Hi,

I have recently decided I need a shorter domain name for my site:
http://networkingpeople.biz

So, I have purchased a new domain and pointed it to my homepage:
http://nppl.biz

With Domain mapping plugin setup and working fine, I am wondering if it is a doable solution to map the main domain from networkingpeople.biz to nppl.biz?

Or, should something more comprehensive be done?

Thanks,
Derek