Since your doctor has seen her twice already and said it's normal, that is reassuring, but I understand the worry never really goes away as a first-time mum. It might still be worth mentioning again at her next visit, or even asking for a referral to a PD who can take a closer look, just so you have more peace of mind. Some babies do have this kind of cough when they are active because of how their airways are still developing, and if there are truly no other symptoms like fever, runny nose, or feeding difficulties, it is generally a less urgent sign. That said, since it has been going on for a few months, a second opinion from a PD never hurts, especially if your gut is still telling you something feels off.