Yes, Zola does sell custom domain names. Custom Domain pricing starts at $14.95; you can click here to purchase.
Once you've completed the purchase, follow these steps:
Follow these steps:
Head to your email and look for the subject line 'Zola Domains Order Confirmation'
Inside the email will be a section called 'Product'. Click on your custom domain name listed underneath:
Click on 'DNS' and select 'Forwarding'
On the right-hand side of the Domain title click on 'Add Forwarding'
Enter your Zola URL (please note: all Wedding Website URLs begin with http://www.zola.com/weddings/(YourUserID) & select 'Temporary 302' and then be sure to select the save button. (The reason 'Temporary' should be selected is because you likely will only want to own the domain for a brief period of time)