If the photographer is any good then her running around wont be a problem and will even make for some better shots.
I used to encourage the kids to run around and be silly because to me the best photos are ones that catch their spitit and personality, if a child is just sitting down possing its not the real them, you want to remember them how they where realy, cheeky, hyper, playfull and I used to get praised very highly for my candid shots with parents saying I had caught their personality so well
Take some of her faverite toys, they are handy for bribing and she is more likely to feel comfertable with something familier and show her true self plus her own faverite toys are often nice to capture in the photo as well especialy if its somthing like a first teddy so you still have that part of the memory in years to come as well.
Some things we used to play around with (we had our own but parents brought some along as well) are things like tutus, fairy wings, faverite teddy.
I lovely one that always turned out nicely was fake scattered rose pettels or holding a big large artifical flower.
Also maybe take a bottle of bubbles with you, most of this is stuff most studios will have (apart from personal toys) so chack with them what they have so if they dont you can take something with you.
I wish I could post some of the photos from my portfolio from the studio photos I used to do to give some idea of differant things but I dont think its fair (and probably very illigal)to post photos of other peoples children on the internet when I only had their permission for a portfolio
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