A couple of years ago Rose wouldn't have been comfortable taking charge either but since her foray into the parallel world where she was the only person with a key to the TARDIS--the only person who cared and realized the TARDIS was a living thing--she's become accustomed to it. Bossing around all kinds of military personal prepared her for taking charge in panic moments.

Moments just like this.

"Not far but you look wiped from the spell," Rose is assuming, "And last time I had Mickey to help me carry him. I don't want to drop him. We're going to need help."

Her fingers ghost over the various cuts, scrapes and bruises on the Doctor's face as she talks.