Hi,
Yes, the copy of the token will have haste. That's covered in Gatherer:
Haste is part of the token’s copiable values. Copies of that token will also have haste.
In general, if the effect says the token “has” an ability, then that ability is part of the token's copiable characteristics, but “gains” does not make it part of the card's copiable characteristics.
Nathan Long
Magic Rules NetRep