I would unplug the iron if the cord was not too hot. If it was hot, I'd probably grab a chunk of fabric close by (because let's face it, there's *always* a chunk of fabric close by) and use it as an oven mitt to unplug the iron. I have fire extinguishers located in several areas of my house - the kitchen, the garage, and the laundry room (which is at the other end of the house). The fire extinguishers are ABC rated, which means I can put out burning wood, plastics, paper, grease, gasoline, and electrical fires.
When I was a child, our electric stove started arcing and spitting out flames from the push-button selectors.
As an adult, my husband and I have dealt with several issues: the wiring harness in our washing machine fried and started smoking. We caught it right away because a) we were home and b) we had installed a smoke detector in the laundry room. We also had a defective circuit breaker that came into contact with an unfortunate bug, the circuit breaker was for our hot tub and started shooting what my husband described as plasma 10 feet high. He ran for the fire extinguisher we had in the garage while I called 911. He had the fire out by the time the trucks got here, the firemen told us we would have lost our master bedroom, half the kitchen, and a good chunk of our roof if we had no extinguisher. The repairs were minor - replaced the electrical panel, all the breakers, some of the insulation that was inside the wall, and a coat of paint.
Keep fire extinguishers in multiple locations in your home, and know how to use them. In my opinion, smoke alarms are not enough!
p.s. My grandfather was a firemen, and one of my closest friends is a fireman. They both have told me the number one cause of house fires is toasters, second is hair dryers/curling irons. Unplug them when you aren't using them, yes even the toaster!