looks like an intentional joke to me, seems like she had it in her hand and throws it into the cake after blowing.

Conjecture based on the trajectory of the teeth (upwards arc, not forwards), the timing of the teeth appearance (after the blow and when she starts to lean backwards), and the awkward sharp hand motion that coincides with the appearance of the teeth. I'm fairly certain that the teeth come from her hands and not her mouth at least, just based on the timing and trajectory, so the question is whether or not it was intentional. The sharp hand motion for the release seems to imply it was, and based on her body language beforehand I'd give even odds at least that she was intentionally concealing the teeth, in preparation for the release.