This image was sent in by Suzi, who describes her as 4.5 inches high with no manufacturers markings. She had jointed limbs, stars in her eyes, a green flower in her belly button and a slight green tinge to her body. Her main hair is molded with a central piece of brushable hair sprouting from the top!
She looks more 90's that 80's to me. It is also interesting to note that her pose means she can't stand up on her own and look like she should be holding something.UPDATE!!!
Ian emailed to say that this doll is from Magic Merbabies
. They were produced by Hasbro in the mid 90's. There is not much information available online about them, so perhaps were not a well sold series. There seem to have been at least two playsets which came with dolls as well as the dolls sold separately with lots of accessories.
Angela adds - "I have several of these dolls, they came with a removable fabric tail with a tiny pocket in the front that held a fizzy tablet that changed the water colour. There was at least one playset for these which I have, called "Magic Water Palace" which is a bath toy. In addition to the small dolls as shown on your photo there are larger barbie size-ish dolls as well."