No, you might run another primary that gets updates from your registrar. Or you might run something like split DNS; one internal and one external and then you simply add your nameserver to the list of NS entries at your registrar.
You would not want to update your whois record for your Internet Account if it is dynamic, even if you have two nameservers.
It's best practice to have multiple slave DNS servers (which can pull zone records from one master) that are located in multiple geographic areas.
If I were you, I would not try to configure and run bind there with Qmail, due to the nature of learning curve with both DNS and bind, and the dependent nature of mail to DNS.
Most of what you need to do is going to be possible via /etc/hosts entries.
But if you insist, you can run an additional DNS name server configured for your IP.
See this HowTo:
http://www.howtoforge.com/bind-installation-on-centos