Puppy wants adult food…

Marina (13 weeks old) is obsessed with getting into her older brothers food. She has been on Purina Puppy (not our choice, what she was on before we got her), and we’ve continued feeding It to her, but she FIEN for Grady’s food. We give her pieces as training treats and she’s been handling It well. Her vet appointment is soon, but I’m curious if anybody has personal experience with something similar, and my question would be

• Long story short - she wants adult food as a puppy, can we start transitioning her over in her daily meals?

Thank you!