Will this power supply damage my gear?
The amp ratting specifies how much current the power supply can source to your device, if the device does not need it all then it wont use it all. So if you have a supply that is 12V at 5A and your device only needs 1A then it is fine since your device only draws as much as it needs. 

Edit: YES like someone else mentioend it is very important to keep in mind the polarity of the connector. If you have a center positive power supply and your device is not as such you are in trouble.