yes, Moskit is primarily intended against smaller targets. It has too small range and too small warhead. For anti-carrier missiles look at P-500/P-1000 and P-700.
While all these missiles are very fast, they also very visible in IR because of their speed, so it makes shooting them down easier, so they expected to be fired like "wolf pack":
http://en.wikipedia.org/wiki/P-700_Granit :
"The missile, when fired in a swarm (group of 4-8) has a unique guidance mode. One of the weapons climbs to a higher altitude and designates targets while the others attack. The missile responsible for target designation climbs in short pop-ups, so as to be harder to intercept. The missiles are linked by data connections, forming a network. If the designating missile is destroyed the next missile will rise to assume its purpose. Missiles are able to differentiate targets, detect groups and prioritize targets automatically using information gathered during flight and types of ships and battle formations pre-programmed in an onboard computer. They will attack targets in order of priority, highest to lowest: after destroying the first target, any remaining missiles will attack the next prioritized target"
