The Girl Genius Paper Doll App was created as part of the Girl Genius and the Rats of Mechanicsburg Kickstarter project, as a bonus for supporters, so they could have a game to play with right away, since the main video game wasn't ready until later on. Unfortunately, the Paper Doll app is no longer available in the Apple store. It was written as a 32-bit app and was never updated to 64 bits, so it won't run on any recent version of iOS and was dropped from the Apple store. An Android was promised at one point, but it is not clear if it was ever produced, and, if it was, if it is still available for Android devices.
The app allowed you to to play with electronic versions of the paper dolls, created by the fashion clank (featured in the Revenge of the Weasel Queen side story), which you could dress in different outfits and superimpose over various backgrounds, as well as combine with your own photographs (on devices with a camera). Initially the app only featured paper dolls based on the original four that have been shown in the comic, Zeetha, Agatha, Krosp, and Gil.
Phil promised to create additional paper dolls for the app, as one set of stretch goals ✣ for the Kickstarter project. Since Krosp is the hero of the Rats of Mechannicsburg game and his original paper doll is a joke that portrays him in a ridiculous light, Phil has promised to create a more heroic Krosp paper doll. In addition, he has promised to eventually make paper dolls for Tarvek Sturmvoraus, Bangladesh Dupree, Moloch von Zinzer, Baron Klaus Wulfenbach, Mamma Gkika, Dimo, Maxim, and Ognian.
When version 2 of the paper doll app came out, it included more paper dolls: Tarvek, von Zinzer, the Baron, Bang, and Mamma Gkika. You can view the artwork for the paper dolls and download high resolution PDF images on the Paper Doll page on the Girl Genius web site for some of them.
The Paper Doll app was free, with the the Krosp and Agatha paper dolls included. The paper dolls for Zeetha, Gil, Tarvek, von Zinzer, the Baron, Bang, and Mamma Gkika could be acquired as 99¢ in-app purchases. All backers of the Kickstarter project at the Citizen of Mechanicsburg level or greater were able to download the paper doll app and get all of the dolls available for it for free.