many, big=name famous quilters quilt their quilts on their domestic sewing machine- as long as you have a good straight stitch, a darning(hopping) foot & can lower your feed-dogs you can do it-
it takes practice.
start with small quilt sandwiches (like 12-15" squares -top, batting, backing) and as you get the hang of it work your way up to larger & larger- you will be quilting quilts in no time- there are tons of videos, tutorials for free motion quilting- check them out= and practice, practice, practice.