I've seen enough anime to recognize that she said "I'm going on ahead" and not "Eat my dust."
I'm glad Kikoru isn't just a "tsundere ojou-sama" but has some character and substance to her.
If he was like Kafka, he would know how to use the phone and he wouldn't say "humans are particular about time". Unless we're told otherwise, we're supposed to assume it's a Kaijuu that can transform into a human. His transformation is quite different from Kafka's too.