when my kids have tantrums they seem to be shorter in duration when there is no audience. I will leave the room (my kids are older than 1 year), or retreat a distance to another side of the room and act as disinterested as possible. As soon as the noise level comes down I let the kids know (is as few words as possible) that I am happy to help them as soon as they can calm down and talk to me. As soon as we can talk I tell them that I understand that they are mad and care about what they think - but that I can't help them when they are screaming, kicking, etc.
Sometimes they just need to blow off some steam before they are able to calm down, so the tantrum may still last a few minutes. But when they realize that I am not paying attention the whole enterprise seems a lot less fun.
Believe me, a one year old CAN understand you when you explain that mommy will wait until you have calmed down. Just because she doesn't have the words yet doesn't mean that she doesn't understand yours.
I wouldn't worry too much about her hitting her head - unless you have marble floor or something. If she really does hurt herself then maybe she will begin to get the message that flipping around is really not a good idea. If you are still worried, maybe there is one safe room in the house with carpet or rug, not too much furniture to run into? When she starts to get out of control then you can take her to that room, explain that this is a safer place for her, and then retreat disinterested.
It will take a few tantrums for her to see the new routine. And this is just me 2 cents, but in *my* experience being right there during a tantrum, immediately available to a child who does not know what they want, only reinforces that this is somehow desireable behaviour - my opinion of course.