What class of society does she come from? You mentioned musician a little later but is she part of the upper or middle class already? Where is she performing? If she's a lady of good breeding and proper upbringing then fencing seems like a fine Victorian martial art she would be likely to learn.
Here are several pages about women fencing in Victorian, England:
https://www.pinterest.com/pin/429953095649684571/
http://victorianfencingsociety.blogspot.com/2014/09/the-victorian-fencing-outfit.html
http://englishhistoryauthors.blogspot.com/2012/10/fencing-in-regency-england-could-woman.html
http://www.historyspinner.com/library/womens-fencing-keep-body-youthful/
Teaching a young lady to fence for sport is what a reputable trainer would do. It's no great stretch that she'd think, "Gosh, if I took the blunted tip off of my rapier and sharpened it up a bit one could do an awful lot of harm!" No ethical instructor would consider telling her about this, unless you want them to be having some kind of affair.
Eastern martial arts are peculiar to the Orient and would not have had much penetration into Victorian society until right before Queen Victoria's death. Here is one example of something that did cross over, Bartitsu (est. 1898)
https://breakingmuscle.com/learn/bartitsu-the-steampunk-mixed-martial-art As a happy coincidence, they accepted women into their training schools. Krav Maga, on the other hand, is a modern Israeli art and most definitely wouldn't be taught or known at that time.
Social class was everything back then (and that hasn't changed much today). Fighting was for men and so I wonder where her escort was when she was mugged? Why didn't he step in to protect her honor? What ghastly ruffian would take more liberties than snatching a purse?
If she's of the lower classes then Heaven alone knows what they get up to. One could picture a fishwife or barmaid having a knife on hand and sticking it somewhere soft. Their lives are poor and desperate and they don't have the benefits of a proper upbringing in spite of all the decent Christian societies we found to better their lot. In fact, the less one has to do with them, the better.
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I've talked around this a bit but I hope it's clear that class structure is important in giving an authentic ring to your Victorian-themed story. If you've got a young lady of no means who lives on the edges of society then she's not going to have money to pay for training. She can engage in the oldest profession to barter for some tips but really, having a knife and shoving it into someone seems likely for any number of professions in the lower classes.
Here is some more background detail that may be handy. The Illustrated London News from 1852. This is what people would have been reading at the time if they were literate. There are lots of neat engravings in there that give a slice-of-life view of Victorian London.
https://books.google.com/books?id=V...ce=gbs_ge_summary_r&cad=0#v=onepage&q&f=false