Trying to understand permalinks

I am not currently having a problem, but this question is to help prevent me from having one later!

I’m in the process of building my new site, and since I have a current live site at http://www.mywebsite.com, I’m building the new site at http://www.mywebsite.com/newsite. So when I am linking all my buttons right now, I’m noticing that the permalinks are of course to pages that look like “www.mywebsite.com/newsite/?page_id=1234”

So what happens when I am ready to make my site live and move it to the root of the domain? I’m assuming (hoping?) that I wouldn’t have to manually re-do any of those links, right? Or that the “newsite” subfolder name won’t show up when people are navigating later? I hope I’ve explained my question clearly. Thank you in advance!