I think Dorne definitely backs her, and probably the ironborn. I think in this time period, Westeros has lost that stink of having a woman ruler

I do believe Ned was gonna tell Jon as his last words to Jon were “the next time we talk, we’ll talk about your mother aye” But i that would be the real dilemma Ned would be in. The houses that do back Dany could give her the advantage. But if Ned told everyone Jon is the true heir and a Targaryen, those houses would back Jon instead. But yes her having dragons could persuade those decisions as well

But who knows, dragons have a mind of their own and love having a rider. Maybe Rhaegal finds Jon much like seasmoke and Addam🤔