If you fuse this at 1A, you are likely to have nuisance blows from the current inrush at startup.
What are you trying to protect with the fuse? If you are trying to protect the power supply from an overload, put the fuse on the output, not the input. It is difficult to determine a fuse size that will blow on an overloaded output without having nuisance blows. Check the specs on the power supply. Some have internal overload and short-circuit protection, so you may not even need to fuse it to protect against overloads.
My suggestion would be to size the fuse based on the wiring supplying the power supply, to protect it in case of a fault internal to the power supply. For 18 AWG, fuse it at 7 A or less. 5 A or even 2 1/2 A would work.
Check the manufacturer's specs first for any fuse size recommendations.