I think as long as you pull the seams out so you're working with a truly flat piece of fabric with your onesie, you could have a block with the front of the onesie as dimensional applique. I wouldn't try to put the whole onesie on. It will be too bulky, too heavy, prone to wrinkles & likely to distort the quilt when laundered.
You could use a fusible, but I probably wouldn't (if you do, window it so it's softer -- it will be a little puffy, but I always like that). I'd probably use a water soluble glue like Roxanne's Glue Baste-It to tack it down before doing the applique work. If your machine can do a nice satin stitch, I think that would look great. Maybe use a color of thread that matches a fabric you're using somewhere else in your quilt to really highlight the onesie, assuming the onesie is white.
I should note that I have not put a onesie into a quilt, but I did do a project with the neighbor kids using WonderUnder, used knit kid's clothes & quilter's cotton and it bonded fine. Just double check that the onesie is 100% cotton. I know WonderUnder is designed only to work with cotton. I suspect that may hold true for all fusibles so check the label & read the fusible package! I learned that lesson the hard way on a quilt for a client.
I'd love to see a pic when you're done. It sounds super cute!