I think I understand, but help me fully comprehend this situation I had today

So... I work in a small college as the athletics department's media person. Our women's soccer team played in the semifinal of its conference tournament today.

I think I understand why, but I just want confirmation of the rule to fully grasp this situation.

My team's player takes possession in the defensive half and goes over the top. A teammate is able to get on the end of the pass behind the defense (somewhere bordering end of midfield and beginning of attacking 1/3) and is essentially 1v1 with the GK

GK comes out of the box (clearly out of the box... near the top of the arc at the top of the box)

offensive player goes for the chip shot, but it heads straight for the GK's head, who instinctively puts her hands up to protect her face... but the ball hits her hands (again... clearly outside of the box)

referee immediately blows the whistle... does the slow walk up while reaching in her back pocket and produces a red card to the GK

DOGSO was the official reason stated for the red card by the statistician at the site

I assume it all fits with DOGSO as the offensive player was behind the back line and 1v1 with the GK... and while I believe incidental (trying to not get smacked in the face) it's a handball foul by the GK outside the box... who was the last line of defense against a potential goal.

Am I correct in this understanding? Is red the right card or should it be yellow? I'll hang up and listen.