Is it correct English to say doled out punishment?

"Doled out punishment" is grammatically correct, but it's a slightly informal and somewhat archaic way to describe punishment. It implies that the punishment was given out in a more or less casual or even begrudging manner.

Here are some more formal and common ways to say it:

* Imposed punishment

* Administered punishment

* Delivered punishment

* Enacted punishment

* Meted out punishment

The best choice will depend on the specific context and tone you want to convey.