There are commercially available instruments, that range from an app for your iPhone to a fully commercial “listening” kit. That said, you might be better hiring a qualified audio engineer to set up a monitoring device that records the sound levels in your home (not the actual sound). I have no idea how much that might cost but at the end of the day you will have a reliable record and an independent professionally qualified witness.
That said, I’n not sure who might provide such a service but a deep Google search dug up these guys: Noise in Apartments | Audiometric & Acoustic Services (noiseconsult.com.au) Might be worth a phone call. Good luck!