mixing fabrics Can you mix knit with quilter's cotton?

Can you mix knit fabric with quilter's cotton?

My daughter has a white shirt and the main part has stains but the sleeves and yoke are fine. I want to removed the stained front and back shirt panels and replace them with another fabric but all I have is quilter's cotton.

It may work, but the two fabrics move and hang differently. The front and back will be more stiff with the cotton whereas the sleeves and arms will stretch. You may have a little trouble keeping the sleeves from stretching out while sewing them onto the cotton.
Personally, I think you would be happier if you found some knit. You could even cut the knit from another t-shirt that isn't being worn.
Good luck!