RFID Module with 20 to 30 cm range

Hey guys and girls, I am working on my first real PI project. I already contributed in a robot project with ROS, but now I wanna do something from scratch. To break it down I need a mechanism to scan a RFID chip from a cats collar and open a lock on a successful scan. So much for the context now the problem. Since I am not an engineer and only do software development with very little interaction on the physical level with such technology I don't know how to find the right modules to fulfil my requirements. I bought a cheep NFC module PN532 in hope to make a first sample and implement the logic and test around. Since the range of this module is around 5 cm if you are lucky I would need something with a higher range, since this is meant to allow access to a cat it should probably be somewhere between 20 - 30 cm. I don't know what prices to expect, but let's try to stay "cheep".

I think 20-30cm is beyond what nfc can handle since it's near field communication, it uses very low energy

Search for RFID at 125KHz, they can be detected at distances you are talking about.