Iddat For Divorcing After 2 Days

Assalamu Alaykum Wr Wb,

A girl ran away with a boy 2 months ago. His father performed their nikaah and then told them to leave the city for a few days. They spent 2 nights alone together in the motel and were physically intimate with each other at that time. After 2 days they came back and they decided they did not want to be together. The boy divorced the girl last night. Does she have to sit in iddah?
Also, if she has to sit in iddah, what are the rulings for iddah. Can she leave the house? Can she go to her Uncles /Grand Parents house? Eg, on Eid.

JazakAllah Khair