Most of the artificial cat whiskers appear to be stuff like fishing line, fiber-optic fibers, brush-bristles, or possibly fine thread dunked in two-part resin or two-part silicone. You may find it easier to fabricate your own head, basically a fursuit head. Otherwise, if you want to avoid potentially damaging your doll’s existing head, you need to get some good two-part silicone and some flesh-color tinting. You’ll definitely need to experiment to get it right and mold a thin. You can slap on above her lips and wrapping to part of her cheeks, with your bristles or whatever embedded in that.
I do not know what kinds of temporary adhesives are safe for either silicone or TPE. If such a thing even exists, then you could apply the whiskers like a fake mustache, as noted above. If no such thing exists, then you may need to consider fabricating your own head.
