This is a great quilt. Your daughter will just love it. The white is pillowing because it was cut on the WOF and has a lot of stretch in it. Peckish has a brilliant idea to follow to fix it. In addition, I would use a thin, all cotton batting, like dream cotton "request". Then after quilting your quilt, I would wash it so it will wrinkle up like an antique quilt, making any remaining pillowing look natural. Work hard not to quilt any pleats into it....but remember your little girl will love it no matter what.