Of course, it is possible to get an insurance for tourists for short periods like 1 month or even shorter. There are different insurance companies who offer such a service.
Iran tourism organization has offered a general plan to insure all tourists who enter Iran and cover all possible issues during the stay. It is known as tourist comprehensive insurance plan but has not been executed yet. I am sure when it will go into effect but it can really relieve tourists concerns about traveling to Iran. In this case it is does not matter if you are traveling on your own or individually. You will be under insurance. I hope this one doesn’t take years before going into effect.