Interesting jam. I know nothing of Dejah Thoris or the stories but when thinking on how I would design a Princess from Mars, the first thing that came to mind was Frank Frazzeta's style of fantasy. Something where the women wear next to nothing yet gloriously designed. I can't draw like that. But I tried so here's my attempt at Dejah Thoris as a royal princess of Mars.
I like the design so much, I may re-use it later as part of my own character designs.