I don't think that there's any point in canon, when it would be believable for Kara to become the commander of Pegasus. XO yes, CO no. I can't picture Kara take that job or anybody offer it to her. Maybe if Lee settled on New Caprica and she stayed in the fleet.

I think Kara is excellent at military strategy, planning missions, piloting vipers and thinking out of the box, but that is not all that leadership is about. It is about people and she is not always that good at seeing other people's needs (or caring about them) or persuading people about her plan without yelling or using fists. Command of a battleship requires patience, diplomacy and ability to make compromises, which are all abilities that Kara generally lacks.

I think she's can handle her pilots being killed by cylons but she would really had hard time with some grand and tough decisions. Like Tigh, Kara doesn't want to have the responsibility over other peoples lives and deaths because she's terrified of making the bad choices, which can ultimately make her to hesitate or self-doubt her next decisions, sending her into despair. I think that Lee is also not comfortable with this kind of responsibility but in his professional life he is much more stable and in control and doesn't let his self-doubts or self-pride get in the way nearly as much as Kara.