I would have to agree with everyone and say 'NO'. Just like the physical changes in our body during puberty or menopause, our hair goes through a similar 'change'. Remember that straight baby hair you had on your head as an infant that eventually fell out and grew into a cute kinky 'fro? Well at 4 years old, her hair still hasn't matured enough to be able to handle chemicals or high heat. At around 9 or 10 years of age (pre-pubescent) her hair will start to shed and 'adult' hairs will grow. This new hair texture achieved during puberty/teen years will be the natural hair texture she'll have for the rest of her adult life. That is why it is usually recommended (by GOOD stylists) NOT to chemically alter a child's hair until they've reached puberty (@ around 10 or 11).
For a natural alternative that will alter her texture and make he hair more manageable, try DC-ing her with a chapie con mixed with some coconut milk. I do this for my daughter and her hair is always soft, moisturized, easy to detangle AND comb after wards!