Search for "high side gate drive" ICs/hybrids. That is what you likely want to ensure you saturate Q1 and Q3 if you want to stick with N-channel parts on the high side. A high side gate driver will handle the DC/DC conversion and level shifting for you so that you can apply logic-level inputs while still pulling the gate above Vcc.
There are many h-bridge gate drive ICs available that offer capabilities like higher gate drive currents for the low side FETs and--something very valuable for those experimenting with H-bridges--cross-conduction prevention logic. Cross-conduction will happen if you turn on both FETs on the same side, or if one FET turns on before its partner on the same side finishes turning off. It is almost always destructive to both FETs on that side (since you're basically shorting the supply rails through the two FETs), and can also take out PCB traces, microcontrollers, etc.
As Olin suggests, omit T1 and simply apply your PWM waveform to the FET gates themselves.