How to calculate gate charge time for a mosfet?
The step by step time constants 



I coloured zones for dynamic losses.  

When using a driver with matched impedance to the gate resistance, Rg ;     


During turn-on  Ids almost peaks THEN Vds falls 
During turn-off Vds almost peaks THEN Ids falls.


during these dynamic switching times 
Pd= Vds*Ids is greatest. 



As once written, seek and ye shall find. 
or re-Search, next time DIY.

From your datasheet...

spec: VGS = 4.5V,  RGEN = 6 Ω  You are driving gate with 1k5 instead of 6 Ω , so we use total Gate Charge equation and datasheet specs instead using worst case.

So effectively with a high source R you are driving with a current source Ig=Vgs/R 
 then  from $$ I_g = ΔQ_g/Δt_s , (ΔQ=Q) , Δt_s = Q_g/I_g = Q_gR_g/V_{gs} = 5nC_{max}\cdot 1k5/5V=1us$$     

Yet if we simply used T=RC=1k5*195pf=293ns (typ) (0.3us)  is only 30% typ of the more accurate worst case gate charge times.  

The Miller plateau for a current source gate drive means that from  C=Q/V is Vgs is flat and Q jumps to the right, that means C rises until Vds drops to minimum. This is a negative feedback effect.