At this time (1000 BC) most trade wouldn't be directly across the Mediterranean, but rather would be a ship from a single port basically hugging the coast and visiting a ton of ports on a sort of circuit around the Mediterranean. Say a ship from the Southern Levantine Coast wants to trade with Egypt and the Aegean. They generally don't go straight across the Mediterranean (it's a pretty long way, and the sea can get really rough at a moment's notice). Instead what they will do is go from their origin (let's say they are leaving from an Egyptian port) and they will go about a day's journey up the coast generally within sight of land. For that reason, you get a number of port cities on the coast relying on this regular trade and traffic. A ship might travel, say, between Gaza (or Ashkelon) and Ashdod in one day, and then the next day travel to Joppa, and then the next day travel to Tyre, then to Byblos, etc. At each stop they would buy and sell or barter for whatever is cheap at that location.

We know this was the pattern because we have seen several shipwrecks off the coast of Turkey from this time period, and we have seen their cargoes and been able to source much of the material to its area of origin, and we have thus reconstructed their trading habits. These are mainly the shipwreck off the coast of Uluburun (Pulak, Cemal. “The Uluburun Shipwreck: An Overview”. The International Journal of Nautical Archaeology, 27.3 (1998): 188–224) and Cape Gelidonya (see Bass, George F. "Cargo from the Age of Bronze: Cape Gelidonya, Turkey," in "Beneath the Seven Seas," edited by George F. Bass, pp. 48-55. New York and London, 2005).

It wasn't until the second half of the Iron Age (~700 BC) that ships really started to take large cargoes of a specific commodity and trade it to a specific port. We discovered this through the excavation of the Tanit and Elissa, modern names given to two shipwrecks found off the coast of Ashkelon, Israel and excavated by a team led by Robert Ballard (of Titanic fame) and Dr. Lawrence Stager of Harvard University. These shipwrecks did not contain a large variety of goods from a diverse set of origins, as the Turkish shipwrecks of earlier periods, but rather each contained hundreds of jars of wine, shipped from the Southern Levant, most likely to Egypt. You can read their report here (PDF warning).

All in all, a cross-Mediterranean journey would take weeks, perhaps even months in 1000 BC, due to the stop-start nature of ocean travel at the time. And even when ships began to venture out into the center of the Mediterranean and travel directly across, it still would take weeks to months to make a journey like that you describe.

But it's true that the Phoenicians established trading colonies at the far end of the Mediterranean. They were extremely accomplished seafarers, some of the best in the Mediterranean at the time. That's what their entire economy was based on. Their homeland was in modern-day Lebanon, and they didn't have much land that wasn't mountains, so they had to turn to the sea to make their living, and built up a massive economic empire spanning the Mediterranean. Carthage (of Hannibal and the Alps) was a Phoenician colony, in fact.

Let me know if you have any more questions, and I would be happy to try to answer them.