(Keep in mind, after Avengers before IM3, Thor 2 and all other sequels )
Tony Stark was not parental material, he said the exact same thing to Pepper when she brought it up. his own father was more concerned with precious Capsicle then his own son, so he didn't exactly have the best childhood, needless to say with his "Job" and his lifestyle he would most probably ruin the child by giving him/her the exact same childhood he had, so the answer was no. N-O. he would not be a father and as he drove in his Bugatti with Rhodey at his right, he was sure.
That was before he saw her.
She was dressed like a punk mixed with an archer. But that wasn't what got his attention as he pulled up next to her at the stoplights, it was the fact that she was riding an ostrich. Now you see a variety of animals in New York: Dogs, Cats, Horses... all sorts, but you never see an Ostrich, well you do in the zoo, but never being ridden, and she was looking completely fine about it!
He turned to Rhodey who recognised that half mad look on his face that shows when he has any idea, "Tony! No! you said that you weren't parent material and Pepper hasn't brought it up in months! you can't change your mind now!" But he knew it was pointless, once that look goes on his face, you'd be hard-pressed to change his mind after.
When the lights turned green the girl sped off, with Tony racing behind, and twenty minutes later they were at her orphanage.
Another twenty minutes she was racing behind them to the newly refurbished Stark Tower, Rhodey called ahead and said that Tony had a surprise for everyone.
Five minutes and several speeding tickets later they were in the penthouse of the Tower with the Avengers, Fury and Pepper standing in the middle of the room. They were all shocked, Tony Stark, THE TONY STARK, THE GREAT NON-PARENT ADOPTED!? Pepper was the first to move, she walked right up into Tony's face, and yelled;
"ANTHONY EDWARD STARK! WHAT WERE YOU THINKING!?"
To which he meekly replied;
"SHE WAS RIDING AN OSTRICH!"