Will a 6V 1.8A power supply harm equipment designed for 6V 600-1000 MA?

No. The rating on the power supply means: "This power supply maintains 6 volts between its terminals, and will supply whatever current is required by the device it powers, as long as that current doesn't exceed 1.8A for very long."

Since the equipment is only expected to need 600-1000 mA (that's 0.6 to 1 A), that power supply will support it nicely, and neither the power supply nor the equipment will damage the other.