Do you have the web pages at zoneedit, or are they the name server and the web pages are on your server?
I understand that running a name server can be a hassle, so I let another company do that for me, and I just host the web sites.
But as for your question about needing two name servers, that is the safest way to go. You can be the primary name server, but you should find someone else to act as a back up name server.
I am assuming that you have a static ip, if not, I dont beleive you can be a name server.
Bob