The only way to get the values is through separate test.
#1) Do a longitudinal pull test and measure the strain in the 1 and 2 directions to get the E1 modulus and Poison's ratio (12).
#2) Do a transvers pull test and measure the strain in the 1 and 2 directions to get the E2 modulus and Poison's ratio (21).
#3) Do a shear test to get the shear modulus, G12.
If you need to determine factors of safety, you will need a total of 5 tests: longitudinal tension, longitudinal compression, transverse tension, transverse compression, and shear.