Are there any postgraduate diploma courses around six months that offer stay back options in UK/Australia?

No, a six-month postgraduate diploma in the UK does not typically qualify for stay-back options like the Graduate Route visa.

The UK's post-study work visa (Graduate Route) is generally available only for degree-level programs lasting at least one year. Most UK postgraduate diplomas are nine months to a year in duration, not six months.

If you want short postgraduate programs with stay-back options, you may need to consider countries like Canada or Australia.