[She follows his actions curiously, possibly flashing him a small smirk in return without even realizing it and then she's smiling widely at him holding her to that promise.]

Then I'm glad, corporal!

[Wait, where are you going? Can she follow? She's about to anyway, without orders even, because there's no way she's going to let him out of her sight now. The cat, who's rubbing her legs, seems to be saying the same message. She doesn't mind if Levi doesn't invite her with words, she can follow that kind of silent actions too.

Ehhh? Taking care of her like that now, are you, corporal? Petra opens her mouth. But what about the animals you were looking for - she could help look for them now, but no, that would be almost like disagreeing to go, so she shuts her mouth for that one.

Instead;]

Yes, sir, that sounds great. [She'd thank him later.]

[Now she just leans down to pet the cat for the tiniest moment because there's orders to follow but...] You know, just between you and me, I'd have followed him anywhere even if he hadn't said anything. [but these pets are still like a thank you to the cat before she straightens herself and is actually, really really ready to follow Levi anywhere. And yes, she knows that Levi probably hears those words, but that's okay!]