The image I just added is of the doll that appears next to Alice during IaMP. I think general consensus is that this is Shanghai, though I can't say I'm 100% sure of it. It's the way Shanghai is drawn in all the fanart anyways, which I think is based on this official image. I still don't have one for Hourai though.
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It is possible her popularity with Alice is something just like on the Nanoha series? Take a look on Hayate and Reinforce?