Yes--use stabilizer on the t-shirt--I like Pellon StayFlex--it's a woven fusible that has lots of drape to it so not as stiff as the non-woven Pellon 911F (my other go-to stabilizer). No need for stabilizer on the denim. Be sure you are using a large enough needle for the denim, otherwise should have no problems. Quilting it on a domestic may be more challenging as heavier fabrics all around--use a #14 or 16 topstitch needle.