Do you have a timeline for the desertification of North Africa -- I think the worst of it happened after 700AD when the Arabs took over. Even in modern times there are fertile areas (I worked in the Libyan oilfields in the 60s) and the land was very fertile if any water hit it. Perhaps Carthage would have become a society of expert irrigators.
Cartagena would likely have been the second city in their empire in any event. If they wanted any metalworking industry they would have also made Genoa, Turin, and Santander important centres, so the empire's focus would -- as you say -- have been northward.
Kester.
I don't have a timeline per se. But I would think that around the time that the Arabs arrived sounds about right. However, a lot of the damage was already done by the time Carthage was around.
Unfortunately, I don't think the prospect of the Carthaginians becoming master irrigators is too likely. By all accounts they tended to neglect agriculture in favour of more cerebral trades, and, rather than growing their own food, tended to import it from their neighbours. Rome, conversely, placed a great deal of emphasis on agriculture, (a trait that one could argue survives today in the former Roman Empire), viewing it as a simple, idealised form of living. For instance, Carthaginian soldiers (or, more often, mercenaries) would be paid in solid cash, whereas Roman soldiers were offered the prospect of land. As a result, Rome became a great expert in agricultural engineering. They, for instance, discovered the process of desertification in (IIRC) the C2nd CE. I doubt Carthage would discover the process that quickly, even it is, geographically, much closer to them.
I must say, I'm getting ahead of myself. I am imagining that the 'dark ages' of your scenario will be comparitively grim, especially if agriculture does not develop as fast as OTL.