Rani Padmavati is a very popular character, but to call her a historical character will be misleading, and wrong, based on evidences so far.
History is based on written sources. Now, there can be a paucity of sources. Some later discovery of a written source can possibly overturn earlier versions. But written source is a must. The only two written sources on Khilji are Amir Khusro and Barani's versions. Cambridge history of India compiled a series on Indian history.
Padmavat, the narrative of Malik Muhammad Jayasi, is a literary work from 16th Century. The Jauhar incident as per recorded history is from Khilji's Ranthambore invasion, which took place in 1301.
Ref: Banarsi Prasad Saksena (1992) . "The Khaljis: Alauddin Khalji", in A Comprehensive History of India: The Delhi Sultanat (A.D. 1206-1526), ed. by Mohammad Habib and Khaliq Ahmad Nizami, p. 368.
But folklore attribute Johar to Chitorgarh, which took place in 1303. As per Amir Khusro, the contemporary historian, the ruler of Chitorgarh then had surrendered to Khilji and was subsequently pardoned as well. Around 50 years later, Ziauddin Barani confirms the same in his records as well. There are no accounts of a Jauhar in Chitorgarh by Khusro or Barani.
(Adding some further reflections to highlight where confusions creep in Indian history.)
There is a tradition of oral history and most of the Rajput Royalties have 'parallel' traditions of their own kept through Jains and Bhats. We are no judges of the truths of such. Current standards of history need proofs and so far, these oral accounts of Rani Padmini could not be collaborated with evidences.
The version of 'image' of Rani Padmini in folklore and the actual 'character' of Malik Muhammad Jayasi's Padmavat are also not converging. As per the literary work,
राघव दूत सोई सैतानू । माया अलाउदीन सुलतानू ।। प्रेम-कथा एहि भाँति बिचारहु। बूझि लेहु जौ बूझै पारहु।।
Given the times, Jayasi was alluding to Allaudin as 'Maya'/illusion, Rana Ratan Sen of Chitorgarh as brain/mind and Rani Padmini as a personification of beauty and wisdom. The narrative of Padmavat is underlining the futility of human emotional attachments and how the ebb and flow of time impacts power, wealth, beauty and fate, and everything is constantly in a state of flux. There are no credible reasons to consider Jayasi's work as a historical document. (Though there are more than enough reasons to consider it a great work of art and even social ethics and morale.)
While oral traditions may have some clues in Bhat renditions, but we are yet to come across any specific mention of Rani Padmini of that era in Bhat or Jain traditions either.