Earthquake insurance usually does indeed cover the problems with sinkholes should a sinkhole damage or swallow your home.
Some insurance companies will sell you what is called sinkhole insurance as well which covers exactly sinkholes should a sinkhole open up on your property and damage your home or swallow up your home.
Ask your insurance agent if they sell sinkhole insurance and it might be covered under earthquake insurance by some companies.
Sinkholes that are naturally occurring underground and in the ground are usually covered by insurance companies under the same category as earthquakes or for any other ground movement.
So if you have earthquake insurance then you most likely will be covered for sinkholes under your earthquake insurance but it would be best to speak with your insurance agent to be sure you're covered under your insurance policy.