In the circuits below, C1 represents gate capacitance, the chief reason you can't have nice vertical edges, and why you need Q8 and Q9 in the first place:
simulate this circuit – Schematic created using CircuitLab
Most importantly, I've included power supply decoupling, with C2 and C3, which are conspicuously and sinfully absent from your design. These are critical reservoirs of energy available to accomodate ridiculously fast-changing current demands. Demands that cannot be met by the power supply alone, due to inductance in the various current paths here. C2 should be ceramic. These capacitors must be connected as close as possible to the load ground, the MOSFET's source, and the collectors of Q8 and Q9. All current loops in that region need to be as tight as possible to keep inductance to a minimum. C2 and C3 might seem unimportant, but they can and will make a huge difference in performance.
In the first design I've merged the 10Ω collector resistances R19 and R18 into a single resistance R20 at the emitters. I don't know why you placed them in the collector paths, but it doesn't make sense since Q8 and Q9 are emitter followers.
R11 and R14 are not necessary, again because of the emitter followers, so they're gone. In any case they only throttled much needed base current.
In the circuit underneath I am preventing Q10 from saturating with R21, which also makes R10 redundant. This will dramatically improve Q10's switch-off speed. It also prevents Q10's collector potential (and consequently gate potential) from falling all the way to 0V, alleviating the need for additional clamping to constrain gate potential.
I've also reduced R11, since you need as much base current for Q8 and Q9 as possible.
Here are plots of input and gate potential:
You still have a problem though, take a look at the graphs of gate current:
Those peaks of over 1A in either direction exceed the absolute maximum peak collector current for Q8 and Q9. For the 2N5551, that's only 600mA. While it may work for now, I don't think Q8 and Q9 would last very long. You could mitigate this by using a larger R20, but the price you pay is slower gate transitions.
I forgot to mention the overshoots. These come from gate-to-drain coupling of the extremely rapid rising and falling of gate potential, due to the capacitance between gate and drain.
That capacitance is a real b*tch, and causes many headaches. The coupling goes the other way too; sharp potential transitions at the drain (across the load) get coupled right back to the gate, opposing whatever you're trying to do at the gate. You try to switch off the MOSFET by raising gate potential, but drain goes shooting downwards, tending to lower gate potential instead. The MOSFET can even switch itself back on, momentarily. This is called the miller effect, and is a compelling argument for proper, strong, gate drivers.
Anyway, the solution to these overshoots and miller effects is not trivial. It could be as simple as an RC snubber across the load, or it might require a much better, lower impedance gate driver. Or perhaps there's nothing you can do about it, and you just have to accept that overshoots and ringing are inevitable to some degree. A lot depends on the load itself, and it's a big topic, a big headache.
Lastly, your choice of MOSFET is not great. It's \$V_{GS(TH)}\$ could be as low as 1.5V, and typically these so called "logic level" devices have very high input capacitance. That capacitance will obviously hamper fast transitions.
Since you are able to obtain \$V_{GS}\$ up to the full 20V acceptable for most MOSFETs, you can afford to use a device which is much less sensitive to gate potential, perhaps having \$V_{GS(TH)}=5V\$ or even more. This will often be accompanied by a much lower input capacitance.
Your use of emitter follower Q9 prohibits gate potential from rising above \$V_{SUPPLY}-V_{BE}=30V-0.7V=29.3V\$. In other words, \$V_{GS} \ge 0.7V\$, always. As a result, the MOSFET will always be precariously close to \$V_{GS}=1.5V\$, where it will begin to switch on.
Looking at the voltage graphs above, it's clear that the rising gate potential crosses this 28.5V threshold very late in the curve. By using a MOSFET with, say, \$V_{GS(TH)}=5V\$, the threshold changes to \$30V - 5V = 25V\$, a point which is crossed much earlier. The slope of the graph there is also much steeper, faster changing, meaning that the MOSFET will spend less time in transition from on to off.