If the current designer is doing the hosting and she wants to put up the new site without telling the designer, I'd suggest biting the bullet and registering a new domain -- and signing up for a hosting contract at one of the service providers who are "WordPress friendly" -- see http://wordpress.org/hosting/ for a starting point.
Register a new domain, like my-company.com if the old one is mycompany.com. The new site can be developed as my-company.com.
When it's okay, the new site can be reinstalled on the old server (with the original domain name, assuming the old server meets the WordPress installation requirements), or the old domain name's configuration can be changed to point to the new server.
Both of these require some cooperation from the original hosting service.
Unsolicited advice: For a system like WordPress, I consider access to at least two environments a requirement. This can be implemented with subdomains (and if her current hosting services offers that, you can explore that option here). For certain upgrades you'll want to do a test before changing the production site, hence the long term need for a second environment.