Whether it's a Quick Charge wall charger or not, a smartphone will only accept Amp current that it is programmed to take. If you connect a non-compatible Quick Charge smartphone into a Quick Charge port then it'll simply default to its max charging speed.
With that said, I think dontpanicbobby is correct that coolpad phones aren't compatible with Quick Charge so there's no reason to spend your money there.
However, the charger that came with the phone is not the only wall charger that you can use with the smartphone. I suggest, if you want to; Get a wall charger that is capable of having a Output charge of 5V/2.4A. That way your smartphone is always charging at its max speed and not limited by the wall charger that it came with. Unless the wall charger that it came with has a high output power.
Ultimately, you should still use the charger that it came with but you shouldn't hesitate to use other wall chargers.