The following contains spoilers for Game of Thrones season seven.
Brienne of Tarth understands that the Stark women can look out for themselves, but how much does she know about their takedown of Littlefinger? In the Game of Thrones season seven finale, Sansa and Arya Stark shock Littlefinger when they turn not on each other, but on him. His poetic death at Winterfell sees the Stark children coming together to defend their family. Meanwhile, Brienne is at King's Landing at Sansa's request, which probably isn't a coincidence.
For years, Brienne has been doing whatever was necessary to fulfill her vow to Catelyn Stark to protect Sansa and Arya. That's why she's hesitant when Sansa asks her to go to King's Landing in her place, reminding Sansa that Littlefinger may be more of a threat than she realizes. Sansa says nothing to confirm or deny how she feels about Littlefinger, but it's now clear that she agreed with Brienne's concerns.
Based on that interaction, we can assume that Brienne didn't know about Sansa and Arya's plans related to Littlefinger. She could safely travel to King's Landing, though, because she understands that the sisters — and Arya in particular — are perfectly capable of defending themselves. When she speaks with the Hound in the season finale, she tells him that Arya is alive and at Winterfell, joking that those who truly need protection are people who oppose Arya.
The thing is, we aren't totally sure what the deal is with Sansa's invitation to King's Landing, but in any case, it certainly played into Sansa and Arya's plans. Brienne's confidence in the Starks makes it much easier for Sansa to convince Brienne to travel in her place, and in all likelihood, Sansa does so to make sure that their plans for Littlefinger's death will go off without a hitch. If Brienne had been around, it's possible that she'd have misunderstood Sansa and Arya's fake interactions and tried to intervene, derailing the Starks' clever maneuver.