Honestly it is the best move if you want to see anything beyond the main cities, public transport links the big spots but once you are out on the steppe having your own motor is a game changer. Bring your passport, a valid driving licence, and an IDP is worth having if your home one is not in Russian or Kazakh. Most places take a small deposit online and you pay the rest when you collect the keys, dead simple. You can browse options to rent a car here Kazakhstan on
https://getrentacar.com/en-US/kazakhstan .