As Michael says, "dash" implies you are in a hurry. In the UK though you are unlikely to hear it in this context. More often it would be used in reference to somewhere local - "I must dash to the supermarket before it closes".

I am off to Paris vs. I dash off to Paris These expressions are more common in British English than in American English. I am off = I'm leaving now. Correct: "I'm off to Paris." (OR "I am off to Paris.") dash off = to leave in a hurry or to write something in a hurry. Correct: "I must dash off to Paris." OR "I've got to dash off to Paris." "I dashed off a note to my flatmate before I left."

I think "I am off to Paris" implies you are going there at your own pace, and "I dash off to Paris" is more saying you are getting there as fast as you can. Both are perfectly fine sentences, but I've only ever heard people say something similar to the first sentence. The second sentence sounds a little awkward in English without any context.