how do I drop the feed dogs
 

how do I drop the feed dogs on a 1938 featherweight in order to FMQ?

A featherweight 221 does not drop feed dogs. You can get a plate to cover them.

Actually you would be better to have a 301, 99 if you want to FMQ. Several on the board say that FW's don't FMQ too well. I think I would piece with the FW and FMQ with the 301 or the 201 I have in the cabinet. Bigger harp on the 201 also for FMQ. I think I need to retire so that I can sew more, exp. since my dd bought be a Davis for my Birthday in a gorgeous cabinet ( I have wanted a treadle for a long time).

I was just with a friend at the Houston Quilt Show. She happened to ask that question - the answer - dial stitch length down to 0.

Wouldn't the feet teeth still be exposed inhibiting movement?

When I first found my FW, I was sooooo excited to use it for everything. Especially quilting! I wanted all the attachments and I wanted to FM with it, so I splurged and bought an original feed dog cover plate from April 1930 for $90. Yes, you read that right $90.
I found that FW was great for FM, but quickly learned that its hard on their little motors after continuous use. I no longer use the FW for FM and the $90 plate and am thinking I should sell the plate. I use my 201 or 15-88 for FM now. Big machines for big work. That said the FW would be good for little FM projects, but why bother for the long run, save that little motor and use a bigger machine for the task of FM quilting on projects. Just my 2 cents from personal experience. That said, I have no idea what your sewing with it, so please take my advice with a grain of salt :)

Anything originally made for a FW (or sold by April 1930s IMHO) seems to be hugely over priced. For my FW I use the feed dog cover from the nearest Singer buttonholer. They were made for featherweight as well but cost a tenth of what you paid for the original cover. My 320k is an amazing machine but the feed dogs don't lower and the cover plate ("darning" plate) was missing, so when I'm sewing a button or doing FME (did it last night - amazing) out comes the cover from the $12.50 buttonholer. Same plate fits everything I've tried it on so far, including my "new" 1891 VS2.