The general style at the time was referred to as “Antique,” modified with a size descriptor like “Nonpareil” for smaller text sizes and “Great Primer” for display sizes. There were many variations over time, and by country.
The dollar sign in these specimens isn’t a great match to your sample, but they give you a general idea of the style:
One modern interpretation of the style is Giza by Font Bureau (though it lacks the through line of the $):
Figgins Antique is a revival of the style that also might work for you: