Yes, a Jet Ski can safely be beached as the impeller is hidden. However, it is recommended that you kill the engine before actually reaching land. And beaching the Jet Ski is hard on it's under surface - that takes a toll over time.
A small 1-seater jet ski and a light trailer might weigh as little as 600lbs.A large 3-seater, however, on a heavy or low-slung trailer can approach 1500lbs.
Kawasaki, I think the first jet ski was made in 1974 I believe it was a 440cc stand up. You can find the definite answer at Kawasaki jet ski museum online.