I would handle it like you were going to machine trapunto ... sort of.
Trace the image onto your fabric - but don't cut it. Then sew the batting onto the batting using water soluble thread (you can use anything in the bobbin - and water soluble in the top). Sew on the line that will be sewn under (assuming you are doing needle turn). The trim the batting with small scissors up to the sewn line. Then you can trim the fabric with a seam allowance. Then you can needle turn the fabric under the batting and sew to your project.
If you don't have water soluble thread you can machine baste - but then you'll have to be extra careful when you trim the batting, and of course remove the basted threads.