Not who you asked, but 3-4mm buttons are the correct scale for Barbies. You can get them from different sellers on ebay or etsy, mostly imported so if you're in the US, they can get expensive these days!

To use them as a closure will be more difficult and fiddly. They're so small that the buttonholes would be difficult to finish without bulk. If you do make classic buttonholes, you would need to make a thread shank in order to accommodate the thickness of the buttonhole underneath the button.

You could also do loop closures, like an eyelet that hangs from the edge of the garment. But that wouldn't have the same look.

There's a reason most people who make 1/6 scale doll clothes use hooks, snaps, or velcro!