I agree, the best thing to try and do is to ignore as much of that behaviour as possible. Bloody hard, i know, but she is reacting to attention.
How mobile is your ikkle one? Would she not be able to crawl after you if you needed to move to another part of the room? If so, encourage her to try this and keep talking to her all the time about what your doing - it gets boring but it is effective. Not only does it prevent the tantrums, but it develops her vocab to boot!
Try singing a song that you can sing while your out of the room so that she can always hear you. Play a game where you call her and if she responds (in her own way - giggles, bables, single words etc) then you respond back.
Whatever you do and whatever works for you both, remember to priase her when she doesnt have a paddy.
Good luck
Flower xx