You don't usually need to wait on random mutation. Most populations maintain a significant amount of variation at any one time, and thus can respond, often on time scales of a few years or less, to sufficiently extreme selective pressures. See, for instance, the book The Beak of the Finch which discusses documented, and nearly instantaneous, selective responses to droughts in the Galapagos Islands. (I.e. the results of the droughts were such that the sizes and natures of seeds available to the birds shifted significantly, and so did the average beak sizes. There was already a range of available beak sizes in the population, so differential survival rapidly shifted the average or typical beak size.)
Some populations more than others. DNA studies indicate that dog breeds are less than 300-400 years old. If all you had of dogs were multi-million year old fossils, you would be amazed at the rapid "evolution" of dogs. Quite enough to be labeled separate species.
Suppose all you had were fossils of wolf and Chihuahua. There would be a huge gap in a geologic eyeblink.
Big deal... NOT! This ain't "Evolution", so quit trying to use it as such.
Oops!
I left you guys out of the above
"You don't usually need to wait on random mutation. Most populations maintain a significant amount of variation at any one time, and thus can respond, often on time scales of a few years or less, to sufficiently extreme selective pressures."
Having less amount of variation in the population is the _opposite_ of evolution. In addition, what evidence is there that the variation is the result of random mutation? This is assuming the conclusion.
In addition, are you sure that in the example you give, there is positive evidence of either random mutationor of selection being the reason for the variation? I've read lots of papers that simply use "selection" for any of a range of phenomena, some quite distant from the ideas that Darwin put forth as "natural selection" (i.e. differential survival and differential reproductive ability).