Firstly, a carrier is a naval ship. The Air Force of today tends to be based off of airstrips and other bases, and tends to act in a long-range strike or short-range defense role. Navies are used to project power, specifically with the mobile air bases called carriers. To be honest though, this is a bit irrelevant, as this is space, and not the sea.
I can't see atmospheric-only aircraft being used to support any offensive actions, as this limits their ability to land anywhere except on ships specifically designed to extract them from the atmosphere. As for aircraft already being able to go into space for a short time, I'd say that's more due to the momentum generated by going up at an angle of 45 degrees at mach 3 than any real method of propulsion once in space. Again though, Im not an aerospace engineer.
My main issue though is that, at the moment, and contrary to how you believe the LAF will be seen, I do feel that it is "just another Liberty group". It's not really fresh as an idea, as we saw with the LMC (marines, airforce, different department, same reason for creation). I also feel that we may encounter similar problems with cooperating. This is what causes me to groan the most, as [LN] has been down that well-trodden path many times before. When I hear "seperate command structure", I also hear "will be considered with the same authority as LN HC", which is what other groups have expected in the past, without putting in the effort required for such a position of authority. This was the root of the problems we had in cooperating.
By all means try to succeed, but if you're looking for support, I am skeptical at best. Typical British cynicism, I suppose.