Thank you both. You've made me more optimistic about what it will be possible to do.
I went back there today, took a handful of soil. From my non experience, I'd say it's the sandy kind. All houses around have decent grass then overgrazing or wrong grass sound like plausible hypothesis. We've been in the dry season for a month, it will last until September. I'd say it's a bit early to have an effect, but I'm also new to this region...
I also went to couple of other houses 1 hour away, the soil was of the same kind, so, as you said, I should probably not make this too much of a criteria.
There are like big 5 rainwater tanks (the region being dry, they are attached pretty much to every house to save drinkable water), so irrigation shouldn't be too much an issue. The driest area is also at the bottom of small hill, so having a reservoir up there to water the area might also be possible.