It might be best to ask the vet's office, what they truly want.
Better to get their input, than to later be told, oh these just won't work.
Of course, the vet/staff may not have a direct answer for you. Thus, it may be best to do one as a tester, then get their feedback before you mass produce! You might even make two, but with different battings, quilting density, etc. to give them something to compare.
Assumedly so, they will be repeatedly washing your quilted mats.
Hot water and the laundry detergent (perhaps harsher than what we use domestically) need to be considered in choosing the fabrics/battings that you use.
Good Luck for some purrrrfectly happy kitties!