Ciao!
Urban (US) slang! urbandictionary.com says:
1. doozy something that is difficult or daunting
man that history exam was a doozy! i think i failed
2. doozy Something extraordinary or bizarre. Etymology: perhaps alteration of daisy, and Duesenberg, a luxury car of the late 1920s and 1930s. It's an English expression.
"That footballer's form is a doozy!",
"Man, that one was a real doozy!"
3. Doozy Puts emphasis and significance on a certain thing, can be used in almost an circumstance for anything.
wow what a goal, that was a doozy
that was a doozy of a meal Mrs. Smith
that girl has a doozy of a rack
I imagine that in your context that it means "bizarre".