Migrating blog to new domain name?

I’m using my new blog to replace my current website. Since I didn’t want anyone viewing my “blogsite” until it was ready, I named it the same, with a “/new” at the end
(lanaganphotography.com/new). I first asked my host (Bluehost) about this, they said
when I was ready to replace the old with the new, it wasn’t a big deal (I’m paraphrasing). Now I’m starting to wonder. I just finished backing everything up, but I’m still hesitant to get in over my head. Both the old and new reside on the same server at Bluehost, I’m just looking to move the blog to “take over” as lanaganphotography.com and the previous Flash design can disappear forever. I’d really appreciate some suggestions/info on how to accomplish this.