How do I calculate necessary mosfet turn on/turn off time?
Your second mosfet is beng turned on through R3. F3db = 1/(2*pi*30 pf* 1KOhm) = 5.3 MHz
- full settling occurs at 6 time constants => ~ 884 Khz.

gate cap = 30 pF from datasheet

Replace R3 with PMOS transistor to form an inverter.