Saepe Fidelis has it right. A large part of how Post-War Carthage is constructed depends on how the conflict is concluded. If, as he suggests, the victory at Cannae triggers a general rebellion among the Italian States, then it is entirely possible that he could successfully march upon and probably take Rome itself.
I don't think that is likely without some kind of stimulus however, as Hannibal's entire strategy revolved around them doing just that, and they never did. In order for that to happen something else would have to occur first. I think a more plausible point of divergence would be the early death or political defeat of Quintus Fabio Maximus, who was the progenitor of Rome's policy of denying Hannibal open combat. If that strategy had not been implemented it is not outside the realm of possibility that Hannibal could have inflicted a string of defeats upon an unprepared and poorly led Roman army that would have caused the rebellion he was looking for.
In terms of post war, I think the treaties would proceed relatively close to what Saepe describes, with Hannibal personally arranging most of the post-war treaties. It's true that the Carthaginian Suffets would look poorly on a conquering general r usurping so much of their power and authority, but given their neglect of his army and efforts during the war this would be entirely in-line for Hannibal. It's probable that upon returning to Carthage Hannibal would make use of his veteran army to establish, if not a monarchy, then at least firm control over the city and it's proceedings. This would probably include rewarding his troops with land and citizenship as Saepe suggests. Given Hannibal's own disposition Carthage, wether imperial in fact or not, would begin to lean towards being an imperial power, exerting a much greater influence over the Mediterranean.