First, the girl is red haired. And from what I know about red heads, they are more likely to get burnt. Second, it's very easy to get burnt outside, even if your out there for only 15 to 30 min, depending on the sun's intensity.
Now, as for whether or not the little girl was in the tanning booth or not, that is another story. We really can't assume one way or another, although we all probably have feelings one way or another. But the real question is, why didn't she just leave the girl at a babysitter instead of taking her to the tanning salon?