Good news is that we don't have to start from scratch when it comes to big data and gender disaggregation: many companies have been investing in lots of ways to parse big data to determine gender. For example, speech patterns in some languages allow identification of the gender of the person.
When it comes to call logs: women call longer, move less, get called more than making calls, and are more likely to call from home during the day.
With info like this can figure out things like: is a drought causing women specifically to travel further to collect water.
As for challenges:
One is that this disaggregation of big data can't be open. It can't be shared in its raw form for risk of reidentification of individuals.
Consent is also an issue. Especially how informed it can be when we don't know what the outcomes of such analysis might be?