Yes, you can buy domain names without buying/having a HostGator hosting plan.
Register with HostGator/LaunchPad
To do so, please visit https://register.hostgator.com/ and purchase the domain you want. The domain registry tool requires credit card payment and is limited to .com, .net, .org, .info, .biz.
Register with HostGator/eNom (Registry Rocket)
You can also register .ws, .us, .bz, .cc, .nu, and .tv online via Registry Rocket.