Suggest you go over to the any of the Traffic Police (Maroor) office and talk to the captain. He will give you all the information. They are usually very friendly, cooperative and helpful people.
Oh and yes, he can rent a car too; they'll probably just want to keep his passport or credit card details or he may have to make a security deposit to cover liability.
Short answer is 'yes'; long answer is 'yes' too but since I'm not entirely sure, you can wait for some other replies too; if I remember correctly, omani licenses are valid all across the GCC and if your friend does shift to Qatar, he can also get the omani converted to qatari license without needing to take a driving test. But please wait for other replies because I'm not sure if there are a maximum number of days that he is allowed to use the omani license as a visitor in Qatar; but yes, he can surely land and start driving; that much is sure :-)