EDIT: Did a rough diagram so you see what I'm talking about.
Basically you have a pressurized water rocket (pressurized via the valve at the top). However, nothing escapes through the hole in the lid because you have a few layers of tape or aluminium foil sandwiched between the lid and the bottle. The 'trigger' device sits just behind the rocket, with the nail just behind the nozzle and the 'piston' just behind the rocket's fins (ring fins here so they fit in the barrel)
When you fire the spudgun, the pressure will force the trigger fowards. It will impact against the nozzle of the bottle (use a short nail so it hits before it builds up much speed).
Now the rocket's rupture disk has been broken, but the dowel is pushed against the nozzle with such force that not too much water escapes. The trigger is still being pushed by the combustion gasses and so it propels itself and the rocket out of the end of the barrel. Once the rocket and trigger have left the barrel, the trigger will fall away while the rocket accelerates, spraying water out behind it.
Not sure how well it would work but it seems like a workable design.
