It should be OK if only one output ever switches at a time (switch-off is just as much a problem as switch-on) and you have gate resistors to limit the transient current charging/discharging that 38nC to less than the ATmega's maximum I/O pin output current limit (+/-40mA for ATmega328P). However the worst case losses in the MOSFETs may be excessive. Modelling the switching losses is far from simple.
Yes, only one MOSFET is switching at a time, switch on and off of different outputs is sequential and not at the same instant.
Given my datasheet (see below) the Vgs is -4V (for 250µA).
So given your 5V supply I doubt that the 2.5A can be reached safely.
Better choose a real logic-level MOSFET.
I second a logic level MOSFET, maybe an IRLML 6401 or 6402.
I understand, this is a prototype on stripboard and I'm planning to look for another MOSFET anyway which is surface mount for a PCB prototype. Would the FDD4243_F085 be a good option in your opinion? It specifies r_ds = 48 m? at V_GS = -4.5 V and I_D = -5.5 A. Input capacitance is a bit higher, but still around 1 nF. Gate charge is lower, at max 29 nC.
I see the IRLML 6401 and 6402 are surface mount as well, SOT-23. That would be great to have small size, -4.3 A continuous I_D at 25 degrees C and max V_DS = 12 V should be sufficient. Would the SOT-23 package be a problem with power dissipation? Quick calculation for 2.5 A and r_DS = 0.05 ? gives 0.31 W. Specification gives 0.01 W/deg C, so around 30 degrees C temp rise. Would that be an issue to avoid somehow?