The end of combat step happens after combat damage is dealt. You can't use Desert to destroy an attacking creature before it has a chance to deal combat damage.
18-04-2017
wotc
Desert is a land subtype with no special meaning. It doesn't grant the land an intrinsic mana ability. Other cards may care about which lands are Deserts.
04-10-2004
wotc
The ability can be used on any player's attacking creatures. This includes your own and creatures in an attack you are not involved in (for multiplayer games).
Random a card of Magic: The Gathering (MTG), but you can also roll the D20 dice, random a Planeswalker, have fun with the random rules and more.