A full netball match is four quarters of fifteen minutes and takes over an hour with intervals — fine for a league, impossible for a one-day carnival. Carnivals almost always run two shortened halves, typically ten minutes each, which gives a slot of about twenty-five minutes including the changeover and the walk between courts.
From there the arithmetic is ordinary. Twelve teams in three groups of four is eighteen group matches; take the three group winners plus the best runner-up into semi-finals and a final and you add three, for twenty-one in total. On three courts at twenty-five minutes that is seven rounds of court-time, just under three hours, and every team plays three matches minimum.
A full round robin with twelve teams is sixty-six matches — nearly ten hours on three courts, which is why carnivals use groups. If you have more time than that, three groups of four with a longer knockout is the right way to spend it, not a bigger round robin.