More on protection below, but as a fair-skinned redhead, I've had a lifetime of sunburns (some truly dreadful ones as a kid), and am always looking for healing treatments for those who DO get the occasional burn. A recent study shows that GREEN TEA compresses applied to a sunburn actually prevents some of the damage to DNA in the skin that can eventually lead to aging and skin cancers.
Another comforting salve is patting plain, cool yogurt on the burn. Vinegar also cools for awhile. Both need frequent reapplication. Green tea could be added to either of these.
There are lots of clashing scientific opinions about the relative dangers of nanoparticles or chemicals in sunscreen vs. the dangers of sunburns. Google "sunscreen for infants" for links offering both opinions, as well as some probably safer "organic" alternatives.
If you can get SPF clothing in your daughter's size, that's a sensible alternative. Even better would be avoiding the sun during the highest-intensity period between 10 a.m. and 3 p.m. – lower-angle, earlier and later rays are partially filtered by passing through more of our atmosphere. Sun hats are good if she'll keep them on.