Yes, you want to separate power and ground planes onto adjacent layers, to maximize the capacitance between power and ground planes (each plane covers the entire area of the PCB). This requires a 4-layer PCB.Your design uses discrete transistors and passive components. I suspect your design has lots of component leads connected to ground, and only a few component leads connected to supply. If you put bypass capacitors to ground (with tiny lead and track lengths to minimize serial inductance) at all the places the supply is used, a supply trace can work as well as a supply plane, permitting a 2-sided PCB. Your design uses no frequencies above 10.7 MHz (and that is a sinewave not a pulse), so is much slower than modern logic designs (where power plane is a good idea).For one-off prototyping, you can replace a 2-sided ground-plane PCB with ugly construction on one-side unetched cooper-clad board using the unetched copper as your ground plane. I once used ugly construction to prototype a circuit using an ECL flipflop clocked at 2.4 GHz.
