First off, we'll keep it simple. At the time of their meeting in the summer of 1926, it's said that Mrs. Christie had written six books. Checking her bibliography, those books would be:
"The Mysterious Affair at Styles"
[Hercule Poirot, Arthur Hastings, Chief Inspector Japp]
"The Secret Adversary"
[Tommy and Tuppence]
"The Murder on the Links"
[Hercule Poirot, Arthur Hastings]
"The Man in the Brown Suit"
[Anne Beddingfeld, Colonel Race]
"The Secret of Chimneys"
"The Murder of Roger Ackroyd"
Those names in the brackets are the sleuths from each book.
It's almost a shame that the Doctor met Agatha Christie even this "late" in her career. It might have been nice to speculate that he and Donna were the inspiration for Tommy and Tuppence, or that the Time Lord served as a sartorial model for "The Man In The Brown Suit".....