Here is the next chapter! It's kind of a bit short but here it is.
P.S. The two year old Time Tot's full name is Pipermondavarious
The Doctor's jaw fell instantly as he looked the impossible little Time Tot. He was the last of Time Lords, so how could such a young Time Tot still survive? These thoughts were conflicting when he felt her pulling at his trousers, craving his attention. This seemed to snap him out and he bend down and picked her up. When he had her in his arms, she wrapped her arms instantly around his, cooing at him.
Oddly enough he felt protective off her, but he assumed it was because she was his kind. He then analysed her clothing. She was wearing a red shirt with a bright pink hoodie on top and she wore small pink trousers as well. They appeared to be normal 21st Century Earth clothes, which surprised him even more. When he saw a glint of silver, he took out a pendant which was hidden by her hoodie. The pendant had a name on it, which spelt 'Piper'.
He blinked and then looked at her, assuming that her name is Piper or at least part of her name; because if she was a Time Tot than she would have a longer name.
"You're impossible," he said as he looked her, eyes still wide. She simply giggled at that and he could feel mentally that she was amused. That was another thing that surprised him, the fact at how easily she seemed to forge the deep mental connection with him. It was true that he could feel all Time Lords in his head, but it was a presence in the back of the mind, with this Time Tot, he held a deeper connection. One that seemed to be more deeper than normal. Not only that, even though her mind was very new, and unfamiliar, it still felt familiar to him, as if he should recognize her. She was a contradiction.
"How did you escape?" he questioned, mostly thinking out loud because he knew he wouldn't be gaining any answer from a two year old toddler.
He simply shook his head, swallowed his shock and turned, deciding to go to TARDIS and test to see how she could have escaped when he was interrupted by a new mental connection.
He heard very fast footsteps and turned around. A man was running towards him, he appeared to be in his twenties, wore braces, bow-tie and a tweed jacket. He had floppy hair and his eyes were fully trained on Piper. He didn't stop until he was five feet away from him.
"Ah! Piper, there you are! You're as jeopardy friendless as your mother. My god she would have been very angry if anything had happened to you-" he kept rambling until the man finally noticed the Doctor.
For the second time in span of five minutes, the Doctor's jaw fell again because the man standing in front of him was, without a doubt, a Time Lord.