There is a circuit diagram here http://www.arduino.cc/playground/uploads/Learning/solenoid_driver.pdf that should would work for driving your pump without a relay. The pump motor replaces solenoid L1 in that diagram. The suggested components including the TIP102 transistor should be fine for your app if the pump only draws 1 amp.If you are more comfortable using a relay you can either select one that can operate on 5v at less than 40ma or use the circuit above but replace the pump with the
Can you get 12v1A from a USB port if you step it up
and I also connect it with 5v relay.
Can I used 2 (9v battery) in order to turn on my 12v water pump?