Just after posting the question I found the relevant equation and came to the same figure of 1kW - it seemed a bit too good to be true!
Keep that in mind the next time you're considering installing a "water feature" with a pump, such as a fountain or decorative stream with waterfall. Lifting water (or pressurizing a flow of it) takes a lot of energy.
Looking a bit further ahead, does a micro-hydro system need any sort of speed regulator to compensate for the load to adjust for either constant voltage or constant frequency (or some combination thereof!!).
Trying to regulate the volatage and frequency at the genny puts you in the same game as a power company. They can afford to throw a lot of resources at the problem - and the amount of resources needed is the same whether it's for 1,000 watts or 1,000 megawatts.
IMHO unless you have a water power resource far larger than the maximum load you're ahead to skip trying to regulate it for direct application to the load (which could lead to frequency instability, brownouts, surges, and overvoltage events). Instead use it as a charger for an otherwise typical battery bank/inverter system. Let the inverter manufacturer deal with the problems of voltage and frequency regulation.