Graphene is already old in that we have had in the lab in very small samples for a few years. Its not quite as strong as carbon nano tubes however. Also its not stable in a flat configuration over on a small size. It will roll onto itself.
Its strength is very high, but as always bulk material strength is always much less than microscopic “bond” strength due to imperfections that cannot be avoided due to thermodynamic reasons. There is at least one paper that suggests that strong enough fibers for a space elevator with CNT will not be possible.
Also bear in mind that if you have something 1/2 enough strong for a space elevator, making pretty impressive rockets are quite easy.