Winging it at the airport during the holiday rush is a proper gamble, you can get stuck for ages while the best cars vanish. Plenty of visitors sort their car hire way ahead of landing, especially around Moscow in early May when everyone and their dog wants a compact with full cover. Just pick a car, lock in the price and grab it at Domodedovo while the walk-in crowd is still scratching their heads. You can browse what's left for your dates on this aggregator
https://getrentacar.com/en-US/russia/moscow .