She most likely has pinworms, which are transferred from other children quite commonly. It is very easy to pass this to other family members. Speak to your doctor or pharmacist. The medication is generally ovet the counter. This is not serious and easy to treat, but all bedding, towels etc. will need to be washed in hot water. Sometimes it is recommended to treat other children or family members. Other signs of pinworm infection include anal itching, especially at night when the female comes out to lay eggs. This is a yucky thing to deal with but , again, not serious, although it does need to be treated.
And no, worms are not aquired from the family pet! She most likely picked it up from a classmate.