There's a good chance that EY didn't want to allude to any historical event. Maybe his writer's instincts to give concrete examples kicked into gear, and he made up a fictional event about a fictional society.

But suppose he did choose to allude to a specific historical event. Why would he choose this one?

He would not choose this event because it was a great disaster with many casualties. According to the Wikipedia article, there is no historical record of any deaths from this eruption, and the disaster is overshadowed historically by the 1693 Sicilian Earthquake. If EY were going for famous and lethal disasters, he would be very unlikely to choose this one when there are so many more famous ones.

He would not choose this disaster because it is Italian. Italy was not well defined in the 17th century. If you had to choose some place to represent modern day Italy, you would be far more likely to choose a place in Northern Italy (like Florence, where modern Italian comes from) than a city in southern Italy (like Sicily, which was ruled by the Spanish in the 17th century).

The only circumstance under which I think EY would choose specifically to allude to Etna's eruption is if he needed to refer to a volcano. If EY needed to refer to a volcanic eruption, it's probably about Horcruxes.

"Plan B," said Harry. "Encase the Dementor in dense metal with a high melting point, probably tungsten, drop it into an active volcano, and hope it ends up inside Earth's mantle. Ah, the whole planet is filled with molten lava under its surface -"

"Yes," said Professor Quirrell. "I know." The Defense Professor was wearing a very odd smile. "I really should have thought of that myself, all things considered. Tell me, Mr. Potter, if you wanted to lose something where no one would ever find it again, where would you put it?"

Quirrell could be smiling because someone else put a Horcrux in Etna, but given his history with Pioneer I think it is more likely that Quirrell himself did the deed.

So (finally), after this long inference chance, I have slightly raise my belief that Quirrell is hundreds of years old.