It's fine to let people know that he has an LLB, if you think that's something worth mentioning.  We can do that in the text.  I've read hundreds of articles where reference is made to the person's studies; what they studied is mentioned (e.g. law, engineering, science), and also where they did it (e.g. University of Sydney; or sometimes just the name of the city, unless it's really important to specify Uni of Sydney vs. Uni of NSW vs. Macquarie vs ...).  But, generally speaking, the precise name of the qualification does not merit a mention, and it certainly doesn't merit a postnominal.  It's enough to know that Howard studied law at wherever.  By all means provide details, but beware of turning articles into resumes.    
 :::::::Just on the Rt Hon thing, it used to be the case that PMs were automatically invited to join the Privy Council (and some other people - see Right Honourable#Australia for the surviving ones).  The majority accepted.  Whitlam declined.  Fraser accepted, but he was the last one, and there won't be any more.