Earth has a radius of about 6400 km. That makes half of the circumference about 20100 km.

For something you release to spread all the way around the world in a year requires it to spread out from you at about 20100 km/year. That is about 2.3 km/hr, or about 0.6 m/s or about 25 inches/second.

I've never tried to measure it, but my recollection of about how long it has taken after something nearby emits a strong odor for that odor to reach my nose is that the speed is in that ballpark.