I left my job in late June, and I've been unemployed the rest of the year [not planning to return to the same type of job]. What should I put in the 'occupation' field?

Yes, you can enter your old occupation, "unemployed", or if you plan to work in a specific new occupation you can enter that. 

The occupation field is just used to compile statistics, so it isn't something that will trigger an audit, or change other parts of your tax return.