"Inaccessible" is generally relative. Many books, articles, and periodicals are available for free online through sources like Google Scholar, Google Books, the Internet Archive, academia.edu, etc. A lot of these don't show up through normal Google searches: you have to go through the database, and there are a lot specialized databases out there if you look hard enough. I did a quick scan through the usual suspects and didn't see anything related to the specific volume or article you're looking for, but that doesn't mean it might not be out there - OCR sometimes plays funny tricks on names.

You could also identify a public or university library that has the volume (through WorldCat, for example, or your library's Interlibrary Loan search engine) and send an interlibrary loan request through your school library for the volume (or a scan of the relative pages); you might also email the university library directly: many university libraries have their own guidelines about scanning, including different forms to fill out and, depending on the material, fees. You can also join the Louisiana Historical Society, which has access to all of the Louisiana Historical Quarterly volumes online (or even send them an email explaining you're a student and requesting the specific article; they might indulge you). In extremis you could even try to buy the particular volume online, although that sort of thing can be tight on your budget.

Sometimes, you just can't lay hand or eyeball on a source. If the source is key to the work, that may mean you have to put it on the backburner until you do find a copy; if it's something you cannot put off (a research paper with a deadline, say)...you have to work around it as best you can. This is the "citations game" - working with and citing the sources you have, while knowing that you do not have access to the sources that the work you're citing cites. It's a balance of having faith in the academic rigueur of the sources you do cite, while doing everything you can to verify the information the information in that work independently. The important thing being, if you don't have complete confidence in a source, it is okay and perfectly honest to admit that you think that source X is biased, or sloppy, or incomplete, or that you were unable to obtain access to source Y.

You should make a good-faith effort to obtain the article you're looking for (through one of the methods I outlined above), and if absolutely unable to source it, inform your teacher you couldn't find it, outline the avenues you attempted, and write the paper without it.

This may or may not work for you, but one very effective way of finding obscure articles that you cannot access directly, is to find someone in your circle of friends and acquaintances who can. A few months ago, a friend of mine posted on Facebook that he was looking for a specific article on dog teeth found in archaeological digs in England. I have no idea of why he was interested in that specific subject, but within 10 minutes he had a pdf copy of the article that someone who had access to it found for him. Any chance that you may know someone who has access to a library where there is a copy of that issue?

The other option is to look for a recent article or book on the subject that could include a bibliography with relevant articles that may be accessible to you. This for example:

BUMAN, NATHAN A. "Historiographical Examinations of the 1811 Slave Insurrection." Louisiana History: The Journal of the Louisiana Historical Association 53, no. 3 (2012): 318-37.