No, your website will be hosted at as a subdomain of a domain owned by us. It will appear as something like <yourbusinessname>.onehourwebsite.com.au
However, we strongly recommend obtaining your own domain name. This will be portable between website hosts in the event you decide you want to move your site to another service provider at some point in the future. You will then be able to RETAIN your domain name. Your own domain name also gives you a stable email address that need not change as long as you own your domain name. You will not need to change your email address every time you change your ISP.
You can check domain name availability and purchase an available domain name here: