I always think about crochet as using a thin yarn. To try to get that with thread, I'd go with Aurifil 12wt (extra long staple cotton thread). Depending on how finicky your machine is, you may need to run the 12wt through the bobbin & do it as bobbin work. I found out on my Bernina 350, I can actually load a 12wt in the top (and then put 50wt in the bobbin).
To truly get closest to the look of a crocheted doily, I'd recommend giving Free Motion couching a try. You could use actual crochet yarn with either a clear poly monofiliment or a matching 50wt cotton. They make fancy couching feet for most modern machines, but as long as you have an embroidery foot and a steady hand, you should be fine. You just free motion the design you want & the yarn gets tacked down in that design.