"Juliet," she responded with a cordial smile. However, her smile quickly faded when she found herself at a loss when it came to knowing what to do next. This man had most likely been struck on the back of the head, and the force of the blow must've knocked him out. Miracuously there was very little external bleeding, but it was difficult to tell just how much damage had been done. That was always a good initial sign - no deep visible wound. Unfortunately, that didn't account for any memory loss or permanent injuries he might've sustained. Regrettably, there wasn't much else she could do for him right now.
She didn't want Kate to panic, so she downplayed the potential seriousness of his condition. Even though she'd referred to him as "this guy," Juliet got the impression Kate was somehow emotionally invested in this man. Surprisingly, she also felt a connection to him - one that ran much deeper than it should have for them to be complete strangers. Though she had a general tendency to want to help others and was always highly disappointed when she failed them, so maybe that was all that was happening here. That, on top of the fact that she was still partially in shock from the crash, was probably a more rational explanation for her attachment to this wounded (and strikingly handsome) individual.
"I'll know more when he wakes up. Right now, we need to find a safe place to keep him comfortable." Preferably somewhere along the beach away from the bulk of the wreckage. She'd also need to find an IV or something that would work to intravenously keep him hydrated in the event that he remained unconscious for several days, or God forbid, even longer - assuming they weren't rescued by then. For some strange reason, Juliet felt a sense of being trapped on this island even though they'd just gotten here.
But she didn't voice any of her doubts or concerns aloud. Juliet wanted to keep things as simple as possible to begin with both because her resources were extremely limited and it would require a diligent search to find the materials she needed and because she didn't want to overwhelm Kate.
"Help me move him over there. Then I'll go find some blankets." Or something for him to lay on and perhaps something she could use to construct a tent. Juliet nodded in the direction she was referring - a ways down the beach away from the center of the chaos, but it was still close.
As she started to position herself to pick up the the man's legs, she stopped and peered up at Kate. "Are you all right?" First things first - before you could treat a patient or assist someone else in any way, you had to make sure you were well enough to handle the task. Kate didn't appear to be badly injured, but there could've been something Juliet had overlooked. As for her, the move wouldn't be painless, but she could endure it if it meant saving this guy's life, especially since the transition would be relatively quick.