Hi Mika,
 
I should start by saying that my two kids are boys - who have a very different potty training experience than girls.
 
But I would say, definitely get her her own potty. And I'd actually, if you can swing it, get a few so you can have them in every bathroom in your house and in the car. When they're potty training, there's an extraordinary amount of "sitting and waiting" time and there are also lots of "false alarm" trips. If they're using the big toilet, they need help getting up and staying on and it can get frustrating for both of you if you have to be involved all the time. Better to have her be able to access the potty by herself quickly and easily. Also, little ones have to sit in an un-natural way on the big toilet (to avoid falling in!) so if they have to spend a lot of time doing it they start to associate being on the potty with being uncomfortable - a step in the wrong direction! And, as you mentioned, you can make a big deal about giving her the potty which they get strangely excited about ;-)
 
I tried a few different potties with my boys and ended up loving the Bjorn one piece. They sit on it in almost a straddle position and my kids both had a really easy time using it. Since it's a single piece of plastic (instead of having a lid and a removable cup, etc) it's really easy to keep clean. The small seats that sit on top of the large seat are also good for traveling and visiting other people's houses. Plus, it's good for them to use the big potty (on a small seat) sometimes so they don't have trouble transitioning to the big potty when they're ready. I do have a couple of friends who's kids resisted giving up their potty chairs because they'd NEVER been on the big potty and had developed a little fear around it.
 
Good luck with the training...such an exciting time!
 
Kat

Hi Mika: In my experience, all kids learn and experience these things differently. "Feel" her out and let her tell/show you what is best for her. I've included a link with some potty training ideas...it might be helpful for you. *I do think that many children enjoy having the small potty of their own...even if it's just for fun :-)