Yes, the Doctor had an ego, but he felt a little apprehension at the level of Jemma's fangirling. He smiled too, but it was less about being pleased, but more about discomfort. Did she think he was a hero? Somebody to be admired and looked up to? But at the same time, he didn't want to interrupt her moment, because this was obviously a big thing for her.
"Yes, I know. I'm the Doctor." The corner of his mouth smirked. "Hello, Jemma. Are you ready to take a ride?" His head tilted to the left, where his TARDIS was parked in the corner of the office, in all her glory.