Don't do it! If her hair is growing slowly now, it will grow oh so slowly after you shave it too!
I speak from experience. It took me forever to grow Ginger's hair out. When it finally got long, I HAD to shave it because her allergies were so bad she was literally chewing patches of hair off
. Anyway, even with the allergies under control now its been months and she still has a very short coat (and I'm sure it's coming in everybit as thin and fine)
Your baby is beautiful.