Likely "'I'm off out" means "I'll go out". I think it is a kind of childish language. In google "I'm off out" hits some 6000 pages. This indicates it's of rare usage. One example is as below: "Tonight I am off out with my mum and sister for a drink and am back at home home tomorrow." paco
I am off out. (I am about to leave) Is it correct ? Yes.
The standard phrase is 'I'm off' The 'out' is sometimes added, as with 'I'm going' and 'I'm going out'. You could also say 'I'm off home', 'I'm off to school or to work', etc.
It's more for spoken English. It's quite an old usage. 'Be off with you!' is an old-fashioned way