Power cables (cords and plugs) are normally covered by separate regulations in each country. Thus, it really does not matter what IEC 60601-1 says, you need to comply with those power cord regulations.
Fortunately, most suppliers of cord sets know these regulations well, so if you buy a cord set with a US plug, it will comply with US regulations. If you buy one with an Australian plug, it will comply with Australian regulations. And if you want to be sure, contact the supplier of the cord set.
Also note that it is possible to argue that in IEC 60601-1, for equipment that uses a detachable cord set, the cord set itself is not part of the "medical electrical equipment".
This is based on 57.3 which says that "EQUIPMENT ... shall be provided with either a POWER SUPPLY CORD or an APPLIANCE INLET".
So, if the equipment has an appliance inlet (for a detachable cord), then the power supply cord is not part of the equipment. This makes sense since of course in the real world it can be used with any detachable cord set.