Rosalind Franklin would never have gotten a Nobel Prize. She died from cancer in 1958, three years before the Watson, Crick and Wilkins were awarded their prize, and Nobel was very clear that his award could not be awarded posthumously. Only ~three people have gotten posthumous awards, and all of them were alive on February 1st of the year they got the award.
Wilkins (Franklin's boss) taking her data without her permission and sharing it with Watson and Crick so they could jump in at the end and analyze it faster than she did- and then not even put her name on the paper but Wilkins instead!- is truly classic academic evil. However, even if they had actually collaborated and Franklin's name had been on the paper, she would not have gotten a Nobel, due to the ovarian cancer that killed her at age 37.
Her name is listed in the acknowledgements and she has a paper in the same issue as Watson&Crick. Also, there's evidence now that her data had already been shared in a departmental seminar when Wilkins shared it with Watson & Crick (I believe this is explained in detail in the Eighth Day of Creation, where the author did deep historical digging).
I don't think she would have concluded that the structure of DNA was a double helix with antiparallel strands (that's the important bit).
The person really getting written out of history in this thread is Raymond Gosling, the PhD student, who actually took the famous "Photo 51"[0] that, along with other evidence, confirmed Watson and Crick's pre-existing hypothesis about the structure of DNA.
As Franklin was leaving the lab, Wilkins became Gosling's supervisor and the rest is history. Describing it as "her data" is not accurate -- the image belonged to King's College, not Franklin personally.
Whether or not Franklin received sufficient credit for her contributions I will leave to others to debate.
[0] https://en.wikipedia.org/wiki/Photo_51