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The reason to use sunscreen at all in children is that two thirds of a person's total lifetime sun exposure comes in the first 18 years of life. The result of excessive exposure and especially sunburn in early years is a greatly increased risk of skin cancers in late adulthood, as well as the cosmetic damage to the skin that the sun's ultraviolet rays inflict.
Of course the best sunscreen is staying indoors, followed by appropriate clothing. Barring these as alternatives, your child needs a good sunscreen applied often if she's going to be out in it. Reapply after swimming - even the "waterproof" ones. SPF 30 seems adequate; I've read that ratings above 30 probably mean little more actual protection, and the FDA is reexamining labeling of sunscreen products claiming very high SPF numbers. How young can you use sunscreens? It has been said in the past that sunscreens should not be used on babies under 6 months, but there is really no lower age limit. See sunglasses
And for your edification, some more philosophical thoughts on the topic of sunscreen.