No, you don't have to have a foot on your machine to FMQ, but personally, I think it makes it much easier.
You can go to Google and type in the brand and model of your machine plus Manual, and you should be able to find and download a manual for your particular machine. This will tell you where the feed dog control is (if there is one).
You can go to www.littlefoot.net and get a foot for FMQ and darning for a really good price. It's actually called a Big Foot, and they have them for both low and high shank machines.
Good luck!