Yeah! that would be great if you told me about stability and how to stabilize it! would you put the fins under the cone??
The basics of stability are that you have to have the Center of Mass (also called Center of Gravity) above the Center of Pressure on the rocket. 1 diameter is usually recommended on model rockets. The simplest way to determine center of mass is to load your rocket with both the egg and water, and then suspend it from a string, and find where it is balanced on the string. To find Center of Pressure you can just make a flat cardboard cutout of your rocket and balance that, which can probably be done on a finger. You then mark the Center of Pressure on the bottle at the same location it is on the cardboard cutout.
If the center of mass is behind the center of pressure then your rocket won't be stable, and if they are relatively close together then it is only marginally stable. To increase stability you have a few options. You can make the rocket longer, make bigger fins, or add more weight to the front. I prefer to make the rocket a little longer, because about one extra bottle length really helps.
I'll try to post some pictures of how to do this in the next few days.
I am a practitioner of the art of magic known as science.