If Renegade Doppelganger becomes a copy of another creature, it copies exactly what was printed on that card and nothing more (unless that card is copying something else or it's a token; see below). It doesn't copy whether the original creature is tapped or untapped, whether it has any counters on it or Auras attached to it, or whether it's been affected by any noncopy effects that changed its power, toughness, types, color, or so on.