I think the implication is that the "Dummy" robot was Tony's very first invention. Which explains why he kept it around all these years. He even bothered recovering Dummy from the ruins of his home at the very end of Iron Man 3.
I liked all those neat things in the IM movies that made them feel more real.
Funny how Tony says no one has ever called him nostalgic in IM1. Recreating all those previous versions of the IM suit, and keeping his arm robot AI around points to him really caring about his past creations.
Pretty sure that line was meant to be sarcastic, since the next thing he says is to tell Dummy to clear all the "junk" off his desk, including the picture of his father. I mean if he's not sentimental then that picture wouldn't be there in the first place, no?