I would not remove the feed dogs. My older machines have the button on top to release the pressure on the presser foot. If you release that pressure, you may be able to do free-motion quilting. If you are going to cover the feed dogs, I recommend something that makes a "bubble" over them, like the plastic cover that comes with some machines. If you don't have that, you might try the plastic cover from a package of Schmetz needles. Position that upside down over the feed dogs, and then tape it to the machine, preferably covering that with a piece of template plastic first, so your quilt doesn't catch on the edges of the Schmetz cover. But you can only do that if you can release the pressure on your presser foot.
It's especially important to use the spring foot (darning or freemotion quilters foot) if you doing this, because it has better flexibility and your quilt will slide more freely.
I hope that helps. :wink: