If they can comfortably lift 1 ton of conventional explosives on their existing missiles, that's not a problem for them.I think the issue for Iran will be delivery rather than bomb making. If they can't nail miniaturization to fit the warhead on to one of their BMs then it's all pretty meaningless.
I think that's partly why they released the "all our missiles going to Israel will have at least 1 ton of payload" message earlier