Yes, that is correct. However, there are multiple ways you can say that sentence and still have it mean the same thing. You could say, "Today, I am taking the day off." (technically, this is not grammatically correct, because you should not end a sentence with a preposition, but it is very common to do so in casual speech.) You could also shorten the sentence and say "I am taking the day off." or "I am taking today off." Any native English speaker will know what you mean. At least in the United States.

"I'm taking the day off" This is the most common way to say it. It is perfectly acceptable to end a sentence with a preposition in speech or writing. This is one of those myths that won't die.