Technique Tips for Photographing Dark Skinned Dolls?

I would say she needs more light on her face, which can be as simple as getting a white piece of paper to use as a reflector that’ll bounce some light back at her. You can also tap her face on your phone’s camera when you’re focusing to tell the camera to meter based on her coloring and not the lighter doll behind her. (That’s how it works on my phone, anyway.)

This article has some good suggestions based on actual people that might be helpful.

 

I second the idea of using a white sheet of paper to bounce some of the light on the doll's face. You can also use a secondary light source but you'd have to have something semi-opaque in front of it to diffuse the light and make it softer.
It's true that you can set the exposure by tapping on an area on the screen, but if you do that on something dark, that usually means that the automatic exposure will blow up everything lighter which isn't good.
The picture you posted seems to be lit by a ceiling light (it seems to come from the top?) and sadly ceiling lights rarely give you a flattering picture because of the way the light is oriented. It's better to get dolls lit with a table lamp or something similar, this way their faces will get enough exposure from the side. Also mitigates the big wig problem you mentioned.

 

Seconding that adding a light source at a different angle will make photographing dark resin (or doll scenes in general) a lot easier, an additional cheap dim lamp will already help a lot in a situation like this. Another good cheap reflector option is wearing a bright white t-shirt as that will reflect light into what you're capturing.

Post-production wise: if you take photos on a tripod (so the camera doesn't move), you can also take 2 photos at different exposures and edit them together later, that's especially useful when you have dolls with contrasting skin tones in the frame. Photographing darker resin is not so different from taking photos of darker skin so all tips and tutorials on that would be relevant as well.