Normally, when a token is created by this ability, it will simply be a Myr Propagator, so it'll also have the token-creating ability. (See below for weird exceptions.)

Here's the detailed version of what happens. As the token is created, it checks the printed values of the Myr Propagator it's copying -- or, if the Myr Propagator whose ability was activated was 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 Myr Propagator, nor will it copy other effects that have changed Myr Propagator's power, toughness, types, color, or so on.

If Myr Propagator has left the battlefield by the time its ability resolves, you'll still put a token onto the battlefield. That token has the copiable values of the characteristics of Myr Propagator as it last existed on the battlefield.

Here are the weird exceptions promised above. If any copy effects have affected the Myr Propagator whose ability was activated, they're taken into account when the token is created. For example: If Myr Propagator's ability is activated, then Myr Propagator temporarily becomes a copy of another creature before its ability resolves (due to Cytoshape, perhaps), the token will be a copy of whatever creature the Myr Propagator is currently a copy of. After the turn ends, the Cytoshaped Myr Propagator reverts back to what it was, but the token will stay as it is. Also, if the copy ability of a creature (such as Cemetery Puca, perhaps) makes it become a copy of Myr Propagator and gain another ability, the token created by this creature's ability will be a Myr Propagator with that additional ability.