As mentioned before, you can use X-ray photoelectron spectroscopy. If your layer is thicker, you can get information about the chemical composition in the first 10nm of your samples. Furthermore, depending on the length of your layer, you can also make a sputter depth profile (to see the dopant distribution inside your layer) - is possible the Ar+ sputtering can interact with your Al (oxidise it) [see attached link].
If the quantity of dopant is within the detection limit, you can also try EDX. However, if you have really low amounts of dopant (< 0.1 at%) - most likely both EDX and XPS will not detect it and then more sensitive techniques should be used.
1) You can try simply the qualitative technique EDS for compositional analysis normally available in most SEM machines, and detect the presence of Aluminum.
This will no doubt depend on the al percentage in your grown film, and the resolution for detection.
2) In case you are able to etch you films, try Atomic absorption spectroscopy.
3) Normally ZnO films are quite resistive. But when doped with Al, they do become conducting, you can measure the surface conductivity using the simple four probe technique. If your conductivity goes very high, you can use a simple multimeter.
4) Just check the literature if there is a different in the refractive indices of pure ZnO and AZO films,. They try out the simeple UV visible optical transmission measurements. also check the band gap changes by doping ZnO with Al, and determine the band using the UV-vis measurements. If lucky you can also determine the changes in the refractive indices by observing the fringes in the transmission spectra