I don't think there's any precise information on this topic in the books, so I'm willing to take answers from any canon material (including movies and any official art).
Do we know what Hogwarts students wore in the 19th century? Has the uniform changed since that time?
I know it's a super out-there question, but it's for writing fanfiction; I need to know if there's any canon information available, and if not I'll just make it up.
TL;DR: there's no official version I can find, but wizarding fashions have certainly evolved. The wizards we see in movie canon appear to be wearing either Renaissance-style robes, or 18th-20th century suits. Ghosts and Chocolate Frog cards show clothing from other eras, and the Hogwarts uniform in the 1940s was quite similar to the uniform in the 1990s (and appears to be based off a standard school uniform). In short, there's a whole bunch of styles used throughout canon that you can use to inspire your clothing.
As far as I know, there's no official information on 19th century Hogwarts robes. However, based on your definition of "canon", there are some relatively official sources that do indicate that wizarding clothing does progress over the ages, although it does remain outdated compared to Muggle clothing. Here's an article by JK Rowling on Wizard clothing, for your interest (although it doesn't answer your question).
10th/11th century (approx) - Helena Ravenclaw/the Grey Lady [movies]
We see the Grey Lady wearing two outfits. One is in the Philosopher's Stone, where a ghost who is assumed to be the Grey Lady is wearing a hooped dress (distinctly not 10th) when talking to Nearly Headless Nick. Later, once the Grey Lady's origins are revealed as the daughter of Rowena Ravenclaw in Deathly Hallows, she's seen with a simpler dress, which is presumably more inkeeping with her actual era. (Note that the Bloody Baron is also seen in the films wearing a 17th century style dress, inspired by Captain Hook, before it becomes known that he was actually from the same time period as the Grey Lady.)
15-16th century - Cornelius Agrippa [video game]
One of the Harry Potter video games includes an image of Cornelius Agrippa's Chocolate Frog card, in which he is seen wearing a Middle-Ages-style cowl (which has been around since at least the 4th century, according to Encyclopedia Britannica). Even though wizarding dress is still old-fashioned, I think it's safe to say they've now moved on from Middle Ages fashion (although, Cornelius may have been some strange outlier).
15th Century: Nearly Headless Nick [movies]
Here, we see Sir Nicholas de Mimsy-Porpington, who died in the 15th century, wearing a very Elizabethan outfit (16-17th century). Another example of a costume from this era is fabulously modelled by the cast of Blackadder II, set during the Elizabethan reign. Again, this style is not reflected in the clothes worn by professors or pupils at Hogwarts.
Early 20th century [movies]
We see a picture (left) of Dumbledore and Grindelwald as young wizards, where they appear to be wearing clothing you might expect from "today's" wizards. Their suits appear to be quite similar to Muggle suits from the 18th and 19th century (right).
1920s - Newt Scamander, Fantastic Beasts and Where to Find Them [upcoming movie]
In the upcoming film, based in New York in the 1920s, Eddie Redmayne plays Newt Scamander. Based on the "first look" images that have been released, I wouldn't say his clothing is hugely different to what we'd expect to today's wizards either.
1940s - Moaning Myrtle, Hogwarts Robes [movies]
This is probably the closest you'll get in terms of uniform. The clothing that Shirley Henderson, the actress, is playing to portray Myrtle (as she was on the day she died, in 1943 according to HP timeline calculations) is quite similar to the modern Hogwarts uniform, but does have some differences (the robe is a lighter grey and a coarser material, and the shirt has a rounded collar). See below about evolving school uniform styles. You can also look at Tom Riddle's and Hagrid's uniforms from the flashback in Chamber of Secrets, although interestingly, Tom's robes look far more similar to the modern-day robes (I guess you have to look sharper when you're preparing for evil).
General wizarding robes [movies]
The robes we associate with people like Professor Dumbledore and Professor McGonagall seem to be very inspired by Renaissance (~14-17th century) robes. However, people like Lupin, Arthur Weasley, Tonks, etc. are wearing far more modern (although still old-fashioned) clothing. And of course, the children we see out of uniform are dressed in fairly modern clothes, even wizarding families such as the Weasleys - we see many a hoodie and pair of jeans, although they tend to be simple clothes with fairly natural fibres (no Spanx, for example). Here are some examples of Renaissance robes:
Current Hogwarts uniform [movies]
The Hogwarts uniform in the film (which is what most people picture) is basically a current English or British school uniform with a robe on top. (I think the book is less specific and just says "school robes".) For reference, here's a pretty typical school uniform:
So, your "most accurate" version may be to visualise a 19th century school uniform, with a robe on top. Here is a BBC article on British school uniforms through the ages which may be of use. They illustrate the 19th century uniform with this school photo:
