That depends on the geographical features of the area you are going to work and the material you сan sample. Radiocarbon dating is possible if there is organic matter buried by moraine (peat, soil, wood)- it is possible to get the time of their burial - probably the time of glacial advance. Al/Be method is used if there are stable boulders with quartz on the surface of moraine - you can find the time of their exposure (melting out of the glacier).

I think the best option is cosmogenic nuclides dating. Have a look at the following link which explains how it works with Antarctica examples:  http://www.antarcticglaciers.org/glacial-geology/dating-glacial-sediments-2/cosmogenic_nuclide_datin/

You will find many papers on google scholar. It is often used in erosion studies also.

The main problem is the difficulty to find labs that accept samples. Often, it needs to be done with a collaboration with a researcher who master the technique and there's not a lot of them. It's not like radiocarbon dating for instance with several commercial labs available. 

good luck

Thanks Both for your valuable comments.

You could read "Himalayan glacial sedimentary environments:

a framework for reconstructing and dating the former

extent of glaciers in high mountains" of Benn and Owen (2002).