I am sure this has been asked before but I didnt see any recent ones...
In the job agency is there criteria for job acceptance/promotion? like level or how many books or anything like that? or is it just random?
There isn't a fixed amount of this much intelligence for that much promotion. Just the more intelligent, the higher/more difficult jobs you can get. The only one that is somewhat known, is SAI, which your pet would need at least 500 intelligence to be accepted.