Answer: Cowgirl
We first found out that Gertie was dressing up as a cowgirl for Halloween when she told Mary this, at the dinner table, near the beginning of the film. When Halloween approached, Gertie was shown, in her cowgirl costume, ready to go trick or treating. Gertie snuck out of the house and went to a secret location that her mother did not know about at all. When Mary took a picture of Michael, Elliott, and "Gertie", she did not realize that "Gertie" was actually E.T. since E.T. wore a white sheet. Gertie told Elliott and Michael that she would wait for them, at a drop off point, where Elliott and E.T. would ride a bicycle, into the woods, to help set up a device to call for a spaceship to take E.T. home.