How can I find Gate charge of the mentioned mosfet gate driver?
You won't. The gate charge is a characteristic of the device you are driving. To turn it on you must transfer that charge to the gate, to turn it off you must remove that charge.
How fast you want to do this (your switching frequency) will determine the current that will flow. The peak current will be driven by the gate resistance
Based upon your system needs, you can then design an appropriate gatedrive.
As to whether your shortlisted driver will work... Yes BUT how well depends on your switching frequency and the peak current you want to hit the MOSFET with
Gate charge: 38nC for an 18V swing
on-die gate resistance: 18R
Peak current 6A
An NCP51705 driving an SCT3120ALHR will need a minimum output drive capability of: 1A for an 18V swing. ✔
The design case is 100kHz. The NCP51705 can switch at 500kHz ✔
At 500kHz the needed power to be sourced is: 68mW ✔
This driver chip appears to have the capability to transfer the needed charge at the required rate