Yes, you can do it. Wiring one quadplex outlet on one branch circuit is the same as two duplexes on one branch circuit. The quad give you the convenience of plugging everything at one location and, more importantly, at one ground point.
A dedicated circuit means the circuit is dedicated to the audio gear -- not the receptacle. Multiple receptacles on one dedicated circuit has the disadvantage of having multiple ground points, increasing the chance of ground loop hum. This is why it's not a good idea to have one receptacle for each piece of audio gear.
A point to keep in mind is that standard receptacles are rated for 15-amps. This is why continuous loads such as space heaters and hair dryers are rated at 1500 watts, or 12.5 amps, because it's 80% of the receptacle's 15-amp rating. Non-continuous loads such as audio amplifiers go over 1500 watts but it's okay to use a 15-amp receptacle because the time at the higher amperage peaks doesn't heat up the receptacle parts. A true 20-amp circuit has a 20-amp receptacle, which has a different blade configuration so a standard (15-amp) plug won't fit into it. You can recognize this receptacle as having a cross on the neutral blade -- to fit the up/down 15-amp plug neutral and the horizontal 20-amp plug neutral. So don't obsess over the "20-amp" circuit rating, because it's not 20-amps since the 15-amp receptacle is the weakest link.
Plugging everything into one quad is fine. Removing the tab on the quad to install two circuits is a waste of money, unless you have a high power amp. Plugging a high power amp into it's own circuit ensures optimal performance into low impedance speaker loads and has no other advantage than that.
