It's been about 8 years since I studied quantitative aerodynamics, but I do remember that drag is an exponential function of speed combined with the coefficient of drag. In other words, as your rocket goes faster, the drag increases exponentially. Also, it means that the smoothness of your finish becomes exponentially more critical as the rocket accelerates.
Eventually you get into a variety of other issues, such as air pressure/humidity, temperature, and drag-induced friction heating. That's why on the high-power rockets that are designed to go well above Mach 1, they use high-temp materials for the nose cones.
So back to the question: doubling the power will have a decreasing effect on your altitude/speed. Yes, it will go faster and higher, but not a doubling.
WW