Dev access for redirected domain?

We have 2 domains hosted on one account. One domain is redirected to primary domain. We will be swapping the domains - redirecting the current primary domain, making the current secondary domain the primary. (so far so good!)

Is it possible to do any dev work on the current secondary (redirected) domain now - before the switch over?

I want to install joomla at root of the new primary and have other clean installs before switching over - can it be done? Or would I be better off switching the domains first and redirecting traffic to the old site while installing Joomla?