Turn your barbie outfit inside out.
Iron a small amount of fusible to some cotton or other light weight fabric - try and keep the hue of the fabric similar to that of the frayed fabric. I stuff the outfit with some rolled up scrap fabric - which makes handling the dress and ensuring you don't get burnt by the iron a bit easier. Peel off the backing of the fusible and iron a small strip onto the frayed fabric.
Now you have 'rebuilt' the fabric - sew the seam. Invisible thread will be your friend here if you don't have a whole host of different cotton colors. I use a combination of a straight stitch and then a small tight binding stitch. Trim any remaining frayed threads bits away.
When you turn your Barbie dress right side out it will look like new.
This method will also help you mend holes and rips in random places that don't have seams.
Don't be afraid to replace ribbon straps, velcro strips and hem dresses shorter where the fraying is out of control. I also can't say enough about snipping all those frayed and pulled threads away. Just tidying up a little bit - can make those barbie outfits look like new again - and give those little hands months more play with their favorite dresses.
I hope this helps you save some of Barbie's favorite outfits in your household!