My 1320's charger is having problem so I am looking to buy a new one. The original nokia charger had a rating of 5V/1.5A output. Will a higher power charger (like 5V/2A) be safe to use?
Yes your phone only uses what it needs.
But if this charger is a quick charger 2.0 than the quick charge part will not work because it's not supported by your phone.
And i would advise to buy a dedicated NOKIA charger or at least a charger of a known brand.