How small is small? Is the school so small that if some kids are identified by the counselor (whose job this would be in our large elementary schools here) as in need, that those kids would be known to all even if things were donated anonymously to them?...Here's what I mean.....
Our school had a Giving Tree. The counselor identified families in need since she knew the families' economic situations and parents didn't. Then she make a posterboard tree with red paper apple shapes on it. The apple shapes would say things that the counselor knew were needed or just wanted by kids in the school -- but NO names were associated with anything.
So the apples might say, for instance:
"Boy's coat, children's size 8"
"Girl's lunch box, Teenage Mutant Ninja Turtles if possible"
"Boy's toy car for age 12"
"Girl's art set for age 8 and up"
"Girl's gloves, children's size 5"
And so on. The tree went on a wall in the front lobby and parents were encouraged to take an apple; get the item; attach the apple to the unwrapped item and place the labeled item in a box under the tree by a certain date. Then the counselor distributed the items to the kids privately, not in front of other kids during school. Only she knew who these specific kids were; the givers didn't.
Is your school so small that this idea wouldn't work because everyone would just know who the individual kids were, even if there were no names on anything? Or are there relatively few families in that kind of need at the school, so this would be identifiable? One way to work around that would be to say that donations will go to a larger charity outside school such as Toys for Tots or the Salvation Army; then the counselor (or a parent leader or a teacher) could include items for kids at the school among a much larger set of "apple" requests for toys or coats etc. for outside needs.
Alternatively, can you find out her birthday? If it's close, get her the lunchbox and say it's her birthday gift. Or a belated one if her birthday was a short while back.
I totally agree with the suggestion below that you talk to the girl's teacher and/or the pastor or whatever official person is in the know about the family's situation. And yes, including the brother would be great. You may be able to donate things to the teacher or pastor and those folks would get them to the kids.
This may be an opportunity for you to start a program at school that helps fill needs for the kids who lack decent coats, gloves, sweaters, or who have no lunchboxes at all....It sounds like you may be being given a nudge to go larger with this and start something bigger at your school.