I would do the stitching first and then do the batt and backing. This way the stitching on the back will be covered. Makes a much nicer looking finished project.

Yes. I would do the design and as an extra measure cover the back of the stitches with an iron on cotton interfacing to keep them in place. Baby items get washed a lot and it will help keep the stitches in place. ECS sell's COTSWOLD BOLTS-Cloud cover Stitch. It should work. Maybe Kristie can give us more info on the product. Always test what you would like to use prior to doing the whole project and you will hopefully be more happy with the outcome.

I would then find a nice cotton or flannel and quilt it together. Then bind.

One thing about the term "iron on". I have found that ironing can and will stretch fabric. Pressing is the key. I say this not as a stitcher but as a quilter. I was the one to do the quilting (putting it all together) in a quilt shop.

Always a quilter who also stitches.

Thanks for the info. Would it be ok to use a 1/8 inch batt and then a piece of muslin and layer it to then stitch the top? I would end by using a fashion fabric on the back and edging it. What do you think of that? Is that ok, too?

Yes you could do that. The idea of the "iron on" is to help secure the stitches so they do not come out. You can forget the muslin and just use the batting and desired fabric or you can just use muslin for the back. If the front of the quilt is white I would be sure to use white batting, otherwise the darker batting will make it look dingy.