There is evidence to suggest that Alexander did have his sights on Carthage. Rome was not yet a powerful state, so he most likely would have had little intent to invade the non-threatening Italian city-states (although that never stopped him before from conquering 'non-threatening' states). To answer your question we have to skim the realm of speculation, since we are considering hypothetical scenarios of his future plans before he had died. But Italy and North Africa were not Alexander's priorities. In the months before his death, Alexander had been preparing to conquer the inland Arabian peninsula. Though Alexander had obtained Anatolia, the Levant, Egypt, and the Near East from Persia, there was a secluded and illusive empire ruled by the Nabataeans, whose capitol city was Petra, located inside of a mountain. This empire has a very fascinating history, and their seclusion is partially the reason why they were not conquered by any of the powerful empires that challenged them. However, their seclusion did not limit their influence. After Alexander's death, Ptolemy who claimed Egypt during the Successors Wars, actually invaded Nabataean lands, but failed to make them capitulate. There was also the Sabas located further into the peninsula, along the Red Sea that Alexander would need to conquer before making any plans for Italy or Carthage. Alexander was aware of their existence and was amassing an army to not only subjugate them, but to also conquer what is today Qatar and Yemen. Before we can consider any invasion of Italy or Carthage, we have to take into account the growing problems he would face in an Arabian campaign, that would inevitably stall or even prevent any Western Mediterranean campaign entirely. Alexander was facing some domestic issues with his army, who were weary of further campaigning. Alexander had led his men to the ends of the known world (for the Greeks) who had already mutinied at the Hyphasis River, but they had again mutinied at Opis in 324 BC. As a result, he began to replace his Greek soldiers with ethnically Persian soldiers trained in Greek tactics. This caused a lot of resentment among the Macedonians who were faithful to Alexander. One of the main issues that divided Alexander from his (Macedonian) men was that he gradually saw himself as not just Hegemon of Greece, but rather, Lord of Asia. This is a topic that has been widely debated, but there are many examples of behavioral changes described in historical texts (Arrian, Diodorus, Curtius Quintus Rufus, plutarch), such as the wearing of purple and Asian garments, forcing his court-historian to "kow-tow" to him, and referring to himself as "Son of Zeus," instead of son of Philip (this last one really pissed off a lot of Macedonians).

So, I suppose to answer your question about Alexander planning to invade Carthage at the time of his death... No, he had no immediate plans to start a campaign against them. It is more accurate to say that conquering Carthage may have been a long-term goal of his. So to put these events chronologically, Alexander would have initially invaded inland Arabia but perhaps without an army of Macedonians. It would have been a majority of ethnic militias and Persian special forces that he would have led to take the Nabataean Empire. Assuming this plan worked in a timely fashion, I imagine he would have set his sights on Carthage. When Alexander conquered the Levant, he sieged the island-fortress of Tyre (332BC), in which the Phoenicians, recognizing that the defenders were losing the conflict, lent naval support to Alexander. Interestingly enough, Carthage was founded by Phoenicians. They were a naval power, and actually made-up the bulk of the Persian navy. I reckon that Alexander, now having the Phoenicians at his disposal, would have forced them into Macedonian service (which is precisely what he did at Tyre), and he would use his role as Archon of the Corinthian League to pull naval forces from Athens and Corinth- which was the source of his navy during the war with Persia, so as much as I hate assuming, there's certainly reason to suspect that Alexander could use his naval coalition against Carthage (which as of 332BCE makes Macedon and Carthage the 2 most powerful navies in the Mediterranean. Historians try not to predict the future, but we can see patterns and analyze root problems, and that right there is a conflict of interest).

The city of Alexandria is also an important aspect of this discussion. Historians have made the argument that the newly founded cultural center of Alexandria can be considered as a hub to challenge Carthaginian influence in North Africa. So, I imagine that would be his next target. There is even evidence that he had threatened Carthage previously, at a reception in Tyre following his victory at Issus. there were embassies from all over the world sent to Tyre to pay respects to Alexander and his great achievement of building a new Macedonian Empire in newly acquired Egypt, and (I believe it was Arrian) that described a slightly awkward, slightly threatening encounter between Carthaginian ambassadors and Alexander. Essentially he made a threat in which he implied, "I'm coming for you next," (I'll try to find the exact passage tonight).

Now the big question is, who would support him on this campaign? Would he have the full devotion of his Macedonian men like he had when he conquered Persia? In my opinion, probably not, and this would prove to be very problematic and significantly delay any plans to commence a campaign against a state as powerful as Carthage.