At a guess, first half of the nineteen-teens.
Technically speaking, this bonnet would probably be better called a cap. By the time this pattern was published, few Quaker ladies were plain dressing and wearing caps, and it's doubtful that those that were would have purchased a McCall pattern to use for making their caps. But late in 1910 the operetta Quaker Girl opened and was very successful. Here's Ina Claire as the Quaker Girl:
The Tyrolean hat, generally in a nice loden green, is still with us, though less exuberantly styled than this version and, if the Google image search is to be believed, much more commonly worn by men than by women. Millinery can be a tricky art, so the somewhat relaxed shaping of the Tyrolean make it a good candidate for a home seamstress with a desire for a casual, sporty chapeau.