Domain help

If I have a domain already purchased can I replace this url with the name of the domain and redirect to this form?

I read something about enterprise...I am only using this for two camps this summer. 

Yes, you have the option to use your domain name on the from URL replacing JotForm, but that feature is only available for JotForm Enterprise plans.

Here is a related guide: How-to-Use-Custom-Domains-with-JotForm-Enterprise 

You may also reach out to our Enterprise support team at enterprise-support@jotform.com if you have queries regarding JotForm Enterprise - https://www.jotform.com/enterprise/