We had this problem at my mother's house, an end of terrace. Next door didn't seem to be able to have a conversation, it was always shouting. And they too got a large dog, even I was scared of it. The dog wasn't too loud, but the shouting to get it to obey was ridiculous.
It's difficult because, as @civicxx notes, when you sell your house you have to disclose disputes with neighbours.
I agree with @theworldistoosmall, an anonymous note isn't really anonymous as they presumably only have one neighbour on either side. It could make the next conversation more confrontational - 'ere, did you write this???
As a landlord, I probably wouldn't throw out my tenants just based on a noise complaint unless it got to the stage of council notices and lawyers.
But if the landlord has an estate agent, you could have a conversation with them without elevating it to the level of a written complaint. Agents usually visit rented properties every few months, but you can also check who advertised the property last time the tenants changed.
One option - invite the parents to visit for a cuppa at about the same time that the daughter is ramping up the noise level. I would play desperate/anxious (baby can't sleep etc.) rather than angry.
Another - as you have had several noisy neighbours, can you consider putting some sound insulation on your party wall? You'd lose about 5cm of the room size but also quite a lot of decibels. It's an American site but have a look at [www.soundproofing.org].
Ultimately, if the tenants change frequently, hopefully you won't have too long to wait before the next change. But it's pot luck who will come next.
Good luck