Does the region need a new coral reef? As that is what it would become in any conflict, the water ways around Israel are far too restrictive.

Given the Israeli penchant for UAVs, I would not be surprised if they were to build a pocket-carrier, similar to the FSF-1 Sea Fighter. It would be able to embark a couple of helicopters, for special operations, plus a few unmanned aircraft, each carrying a couple of missiles. It is not what most would call an aircraft carrier, but it would embark aircraft, capable of carrying missiles.

But Israel does not need a ship capable of carrying aircraft equipped with missiles. Look how large Israel is, then look at the range of F15's. Their aircraft can already project force as far as their furthest potential enemy.

Haha! good one! an Izzie carrier! Khhhhhhh! Yimmy, we'd certainly welcome a coral reef in the Med along our coast, and this becomes a distinct possibility with all that global warming going on, provided we ever get serious about curbing littoral pollution. The water temperature hasn't dropped below 17 Celsius for quite a few winters now, and plenty reef-forming organism's larvae from the Red Sea can reach our shores by way of the usual "Lessepsian Migration Route", that is, the good ole' Suez canal. We do not need, however, to sink anything as expensive as an aircraft carrier in order to help marine life get established, and we have in the past bloob-bloobed down quite a few of our old missile boats as well as miscellaneous other military junk, for precisely that purpose. The Navy here is talking about a couple of air-defense destroyers, which makes solid sense since the IRBM threat is very real, and some have even been talking about the possibility of one of these LHD's, or what do you call them, a large amphib ship that'd carry helos, jumpjets, and a battallion or so of mech troops with their landing craft or what-have-you, that would give us some offensive capability we now lack and I doubt we'll ever need. In the real world, none of this will of course be funded for the foreseeable future, although there are rumors that a long range follow-on to the Barak VL-SAM is under development, in order to afford a future air-defense ship of much modester proportions than an Aegis cruiser/destroyer, some credible ABM capabilities.

With jihadist Iran looming more as a real threat that will have to be engaged... Israeli needs for force projection become greater. Aircraft carriers is one of the ultimate weapons for force projection so the question remains. If Israel were to embark on such a plan what in the very least would it need to produce this? I'm thinking that it would be a small carrier that utilizes vertical take off planes JSF b-variant or harriers. 

Let's be realistic shall we?

Lawman has it about correct. For Israel's naval mission, long endurance submarines to give Iran the works makes a lot more sense as a power projection naval weapon than a carrier.

In the surface warfare department, Israel's needs  we can define by the maximal enemy threat in which Israel itself is the ultimate battlespace.

Air defense and coastal interdiction becomes the primary need.

A 15000 ton battlecruiser is too large, expensive, complex, and too much of a logistic nightmare for Israel to realistically indigenously maintain or sustain.

Procurement requirement.

1. Ship must be capable of coastal as well as deepwater operations in the eastern Mediterranean, Red Sea, and a sortie radius of at least 4500 kilometers.
2. Ship must have artillery bombardment capability inland from offshore inland at least 20 kilometers and preferably 25 kilometers. This means at least a 12.7 centimeterL50 naval gun.
3. Ship must be capable of deploying at least two and possibly four boat inspection parties for stop and search operations.
4. Ship should operate at least one manned helicopter and two VTOL/UCAVs.
a. ASW configurability for the three aircraft  along with ASuW  capability in the manned VTOL aircraft.
b. Flight  endurance of all three machines minmum 3 hours.
5. Anti-air warfare suite should be primary suite for this ship.
a. ABM radar/missile suite sufficient to deal with Shahab IV type IRBM as the referent threat. In fact as I look at the design requirement and the shape of the battlespace, a floating ABM system may be ideal for Israel as it provides a mobile ABM defense that can be moved along the major N/S; E /W threat flightline ballistic missile axes. There must be a realistic expectation that there will be few of these ships or few of these ABMs. So threat axis orientaion and efficiencies become paramount in the procurement decision.
b. SAM radar/missile/countermeasures suite sufficient to deal with the expected BRAHMOS , Sukhoi, Mirage, CLUB, Improved  Exocet, C-801 C-802, etc. type air threats.
6. Close in defense.
a. Auto-cannon for bogjammer and smallboat work.
b. Torpedo decoy.
c. Portable weapons such as GPMGs, mortars,  shoulder-fired missiles, rifles, grenade launchers, and what not, plus a "marine" party that can deploy from well offshore to conduct raids and within port conduct port security for the ship.
d. Capacity to operate at least one , and preferably two or more, UCSVs for offship surface sensor and  surface combat operations. Such UCSVs should at a minimum be capable of sinking a bogjammer and idealy sink a small freighter or a standard Syrian FPB.
7. Optional; anti-minewarfare suite.
a. Mine search UUV.
b. Mine search USV.

These capabilities are the desired ones. Notice that this ship is oriented heavily toward air and surface warfare?m I don't believe that Israel can afford or sustain the ASW-oriented equivalent. Nor should it try. Shore based ASW and corvettes should be able to keep her SLOCs clear. If an enemy of bigger mass comes into the picture then the conflict will draw in the EU and the US as this will no longer be an Israel-restricted war, but a general active maritime trade war.
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Displacement for this ship will be tough. The smallest hull into which you can cram all those goodies is about 5000 tonnes.

That particular dream frigate is beyond Israeli technology at the moment. I suspect the requirement  would be a tough nut for the US to crack, itself.

Realistically the only nations, that could even try to build such a hull are Britain, France, Italy/Spain[with a lot of subcontracted EU help], Russia, Japan, and the United States.

Anybody else? Forget it.

Herald