Learn English – Report on duty or Report for duty

You would use for, meaning "in place of":

1. in place of; instead of" ⇒ to use blankets for coats"

so:

inkorrect is a typo for incorrect.

(In American English) "New Year's" is short for "New Year's Eve" and is usually capitalized. "The new year" means "this next year" and is usually not capitalized. Just saying "New Year" is not grammatically complete, and so I wouldn't know for sure which you mean.

All of the following are possible (as well as many other variations):

What are you doing New Year's (Eve)?

What are you doing for New Year's (Eve)?

What are you doing on New Year's (Eve)?

What are you doing for the new year?

What are you doing in the new year?

What are you doing at midnight on New Year's?

Side note: The first option is the title of a classic "standard" song that you'll often hear this time of year.

New Year's can also mean "New Year's Day", but if you don't specify most people would assume you mean New Year's Eve, because that's when the parties are.