Need a bit more info - I take it this is a new purchase and it's in a pot? I'd ask how large the pot is and how tall the Eucalyptus plant is, and whether there was lots of lichen/moss on the top of the compost in the pot when you bought it?

Eucalyptus need surprising amounts of water in a pot! In a heated greenhouse, you will probably need to water it every day. In an unheated greenhouse, every other day to twice a week is more normal. If it's not in a greenhouse, the frost probably got it!