Translation:У меня нет десерта.
Why must I add "-a" after "десерт"? Is it a casing thing I've overlooked?
You must use Genitive case with the word нет.
I learned that dessert was сладкое some twenty years ago. Is this a normal translation?
Сладкое, though still understood, is an antiquated word. Десерт is the standard today.