Looking at shots on Flickr, it looks like they don't get much closer than a mile to Uluru, and that the helicopters are sealed, ie no open windows or doors. This would I think make the 18-55 would be the best choice. I've not looked at the exif of any shots, but it would be worthwhile searching out images taken from helicopter flights and checking the exif if possible. In my experience (though shooting from planes rather than helicopters), anything over about 90mm on a crop sensor will result in images being blurred in parts, as the windows are not optically perfect at all. I have shot longer focal lengths than that, but you have to find exactly the right bit of window.If you can open a window (I'd be very surprised if you got a flight without doors) then this problem obviously disappears. Be careful of sticking a lens into the slipstream though. If you sit in the front, the distortion from the bubble would be even worse, along with reflections. Wherever you sit, try to shoot through the flattest bit of window you can find that doesn't have scratches. If it's dirty see if it can be cleaned.
Also, as far as windows go (though I've not managed to find any any scientific reason for this) in my experience lenses with smaller front elements tend to perform better shooting through aircraft windows. For example, my Pentax 18-55mm worked better on aerial shots than a Sigma 24-70mm f2.8, which had a very large front element. The Sigma was far sharper on the ground. I've also found that shooting from about 4-6 inches (the closer distance for wider focal lengths) from the window gives the best IQ. Again, I've no scientific evidence to support this, just a lot of experimentation. F8 seems to be the sweet spot on slower lenses, smaller apertures appear to increase diffraction when shooting through windows. However, I must stress that this is from shooting from a pressurised aircraft, with laminated windows, but I'd expect the thinner windows in a helicopter would not be any more optically correct. In a plane, it's possible to shoot at really slow shutter speeds, but I'd expect to have to increase that a fair bit on a chopper. Try to keep your elbows/arms away from the fuselage when shooting and you'll be able to shoot at slower speeds, but if the flight is in broad daylight you should be able to shoot at pretty fast shutter speeds at f8 if you shoot at say ISO 200-400.
If the helicopter obviously has smaller windows that will open, and it's only people in your party on the flight, then you may be able to talk the pilot into letting you open the window. That would be the best option. If it's got the doors open or removed, even better. Then I'd try to take another body with the 70-300mm lens on too.
Have a look at my
aerial images if you like.