Setting up the DNS server on the same physical server won't give you any redundancy. You can either use a 3rd party DNS provider or pick up a cheap VPS and use that as your secondary DNS server.
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Most registrars will host DNS records for domains registered through them. The drawback is you use their control panel for maintaining the DNS records for those domains so it is less integrated with your web hosting control panel.
An example that provides both hosting of DNS records for domains purchased through them and does DNS hosting for names that aren't for a fee of around $5/year is eNom.com