The Deshaker guide, unless I'm reading it incorrectly, implies it works better if you de-interlace first. There's a section with a heading "Stabilizing Interlaced Video".
http://www.guthspot.se/video/deshaker.htm
Maybe you'd be better off de-interlacing to 50/60fps with QTGMC, and given 1080i has roughly the same spacial resolution as 720p, you could downscale to 720p after deshaking and leave it at 50/60fps, and most devices these days should play it, even Bluray players with a USB input, as every player I've come across supports at least High Profile, Level 4.1 in an Mp4 or MKV, no Bluray compatibility encoder settings required.
You mightn't want to downscale, but it might be worth comparing deshaking with and without deinterlacing first, or maybe someone with experience using deshaker (I've had almost none) can offer an opinion on that.