The only opinion I can formulate at the moment must be based on what I've seen of Ms. Whittaker's work, which is playing Beth Latimer on Broadchurch, which, if you haven't guessed, I'm quite the fan of. Beth in particular is one of my favorite characters: she's a slight, willowy woman with a happy life, marriage, and family who is subjected to the worst nightmare a mother has - the violent death of her child - at the same time she discovers that her husband has cheated on her. She initially falls apart, as anyone would do, then picks up the pieces of her life, keeping her family together through the crisis and then through the trial of her child's murderer. I won't spoil the third series, as I know it is still being aired for the first time in the U.S., but she's amazing in it as well. Her tragedies change her and she never is able to return to a normal life - and yes, she makes mistakes like everyone else, especially blaming Ellie for her husband's actions - but she comes out the stronger person.
Do I want Ms. Whittaker's Doctor to be like Beth Latimer? No, I want her to be her Doctor, whoever that is. But she's convinced me that she can play and develop a well-drawn character, and I'm looking forward to her performance. The real question, the one that will make or break the show, is whether or not the writing and vision will support her, and as I've been pleased with Chris Chibnall's work on DW previously, I'm optimistic on that front.