Frankly, i think one of those hand-held water rockets in the hands of a
3-year old is an accident waiting to happen. 3-y olds just don't have the coordination or one-handed strength to point such a rocket in an appropriate direction at the same time they are pulling (usually stiff) trigger mechanism.
The stomp rockets are better, but a 3-y old's mass doesn't make for much in the way of stomping power, and the kids are a bit prone to falling over in their enthusiastic attempts to "jump harder"...
The pump and launch stand based air and water rockets (like the estes air hog rocket, or the nerf rocket launcher) actually work pretty well, with a bit of supervision. They tend to contain devices designed to make sure they are launched only when pointing upward, which a 3-y won't understand very well, leading to some frustration, but it makes them relatively safe unless they manage to hang their bodies directly over the launcher (which they WILL, given a chance. Even "safe" toys need a bit of supervision.) Kids can probably pump them up enough to get SOME flight, and will be impressed at how strong dad or big brother is, and how high the rocket goes with THEM pumping it up... :-)
A 3-y old is well capable of "helping" dad build an estes-style or high power sized rocket (they can at least pour paint on it...), and appreciating a real model rocket launch, even with its attendent safety rules, as long as it doesn't drag out for too long. Bigger rockets are better, but actual HPR motors are likely to be too noisy for most of them... fly with a club, and there's lots of spectating to do in between your own launches.
Finally, there are interesting things you can do with staws, tape for nose and fins, and perhaps an ear syringe. And these "rocket balloons" work pretty well too:
(however, don't forget that balloons are currently villified as one of the most dangerous toys commonly given to small children. Several kids a year manage to suffocate on balloons or balloon pieces that they get stuck in their respiratory system, and the balloon pieces tend to be soft enough that they're difficult to get out via standard first aid procedures. While many small toys are restricted to children over three years of age, I've seen suggestions that balloons are only for kids over
- I think it's a bit ridiculous. Using a pump for inflation rather than the mouth probably helps a lot...)