You most definitely had a Lace doll by Creata, from the second year I guess. I had one of the first year ones in the 80's, and you can find a little info on the page http://rockjem.com/similardolls.html
But for more pictures and to find the exact one you had, check ebay. I just checked and they have plenty of auctions for these particular dolls right now.
I agree they were of higher quality than Barbie, infact especially these days when Barbie dolls have gone really low quality.