Create a website without shutting down the blog

I all ready have created a blog in wordpress and now I am thinking of recreating my website in wordpress as well. My website is put together by rvsitebuilder and the reason I am changing to wordpress is because I can easily change the content, images, add/remove items, etc. of the site in wordpress. This is the site here (rvsitebuilder) & the blog here (wordpress).

My question is how can I “copy” my current site onto wordpress without (1)getting a new account? (2)getting the blog offline?

I want to keep my current account and I don’t want to shut the blog down. Is there a way I can build my site in the backend and then publish the site once completed.

Thanks in advance.
Any feedback will be helpful