You can find a nice book about antenna design: Constantine A. Balanis "Antenna theory Analysis and design"
The problem with low frequency is that it requires much larger size of antenna and more power.
Your RFID can get power supply primary from Near Field region, where RF power density is very high.
It requires low frequency and high power in order to provide power supply for RFID on large distance.
Also it will helps third party to intercept your communication, because Near Field region will be large.
On the other hand, if your RFID has battery, you can use UHF and small directional antenna, but it will leads to another issue. It will be hard to limit distance to 1 meter, because your RFID will works in the Far Field region, where RF power fades with distance not so fast like in the Near Field region. This is not good for RFID, because third party can intercept your communication and even hijack it.
Hmm, maybe I did violate a law of physics.
Yes, if you're trying to use Near Field communication, because antenna radiation pattern exists for the Far Field region only. You cannot create antenna with specific directivity for Near Field communication.
Battery less RFID is designed to work primary in the Near Field region, where you cannot direct the radiation in one direction. Also it helps to receive weak signal, because antenna much more sensitive for weak signal in it's Near Field region. At the same time it minimizes risk of hijack on the long distance.
It will be hard to provide enough power supply in the Far Field region for your RFID with UHF frequency because RF power density will be too small on long distance. So it should use battery and use Far Field region for communication. It means that it will be hard to limit working distance with 1 meter, but on the other hand you will be able to use antenna with directivity, for example Yagi–Uda or parabolic antenna.
Here is picture which shows difference between Far Field and Near Field regions of antenna: