My cat gives my baby her tail

Just as the title says, my cat likes to play with my baby with her tail. She lays so she's pressed up against her and she waves her tail in front of her face until she grabs it 😆 and then I have to keep saving her from the baby pulling on her tail. She is absolutely in love with my baby, my daughter can do no wrong in her eyes. I try and make sure my kid is gentle with her, but even if she's not, she doesn't mind (I still always encourage being gentle, though). She tries to nanny her and snuggle all the time, I'm pretty lucky. But I just thought using her tail as a toy for the baby was really interesting. Anyone else experience this with their baby and cat?