Chewing on her hand...

My daughter is almost 2 months old and has recently discovered her hands. She chews on them constantly and will often spit out the binky to chew on her hand. I am really worried it will lead to her sucking her thumb. (It is not a hunger thing either, she does it all the time). I can't keep gloves on her anymore because she soaks through them in a few minutes and it makes her hands cold and white.

Is there anyway I can stop this now? Or is it already too late?