How can I keep an existing site up whilst revamping it on a new theme? Some advice please

Hi

I’m revamping an existing site for a friend, but want to keep the site up whilst i do it. I’m moving the site onto new hosting anyway (via fiverr.com) and thought that i’d also ask for a copy of the site placed on another domain and use domain redirect whilst I work on the revamp. I am a semi-newbie which is why i’m asking for advice just to make sure my thinking is correct.

Thanks