As the token is created, it checks the printed values of the creature it’s copying -- or, if that creature is itself a token, the original characteristics of that token as stated by the effect that put it onto the battlefield -- as well as any copy effects that have been applied to it. It won’t copy counters on the creature, nor will it copy other effects that have changed the creature’s power, toughness, types, color, or so on.

Haste is part of the token’s copiable values. Copies of that token will also have haste.