Moving blog section of wordpress site to new domain

Hi,
I am moving only the blog section of my current website to a new domain on its own (so gatehealing.co/blog will now go to newwebsite.com (I have not decided if I’ll put pages on the new site and put the blog on newsite.com/blog, or just leave it as newsite.com).

Since I am leaving all of the pages of gatehealing.com as is, I just need to figure out what I need to do to move only the blog over. I have the new domain setup and hosted, have wordpress installed, and have mysql database set up. But I don’t know what to do in terms of the sql database since I am NOT moving the entire gatehealing site.

Is there an easy way to just take the posts from the current site and drop them on to the new site in a way that leaves published posts as published and draft posts as drafts?

Thanks y’all,
Jon

The page I need help with: [log in to see the link]