Yes, it's perfectly easy to do a self-drive Kenya safari. When you ask if it's "safe" that depends a little on what you mean. If you mean are there bandits, car jackings, dangers from wildlife, etc, then no you are quite safe. Instead the danger is from other drivers, as the driving conditions can be a little 'hectic' in places and accidents are common.
I'd recommend hiring a car with a driver, which can be a cheaper and, in my opinion, a much better option. A good driver will know the lay of the land, the driving conditions, best places to stop for lunch, etc. And they are often knowledgeable of the wildlife. A good driver will be both your driver and guide, and probably become your friend!
Almost any tour company in Nairobi or Mombasa can organise a private vehicle with a driver. Standards and prices vary hugely, so explain to the tour company exactly where you want to go and get in writing exactly what is and isn't included. Pay particular attention as to whether fuel, and the drivers food and accommodation is included in the rates. Also make sure you're booking the right vehicle: a 4WD may be needed for more remote areas.
