From your profile, it appears you are in Australia. I would go to one of your local bike stores with a good selection of bikes and get help from them in fitting a (cheap) hardtail bike to her. Maybe a nice little hydration pack, helmet, etc. She will outgrow it fairly quickly in size and, if she likes the sport, in capability.
Once she's tall enough to fit on a 26" wheel bike, I'd be inclined to build up a frame for her, just to keep the weight down.
The more important thing is the way in which you introduce her to biking. Not all kids immediately take to it. Patience, as you probably know, is critical. When I first took my 7 year old son - my youngest - biking, we'd go about half a mile, sit down and have a candy bar and a few sips from a Camelbak, look at the scenery and go home. Now, 20 years later, he forces me to go on 30 mile sufferfests in Utah. It's great!
Good luck.