Edinburgh back-rower McInally will team up with the squad in Newcastle ahead of Tuesday's Test match against Australia, while Glasgow Warriors centre Dunbar is already Down Under visiting relatives.
McInally has been called in as a cover for John Barclay, while Dunbar gets the chance as Max Evans' arrival has been delayed due to his club commitments with Castres.
Scotland head coach Andy Robinson said: "We've called up Stuart as a precaution given a hand injury that John Barclay sustained in training on Wednesday.
"John should be available for selection for the Test but we felt it better to ensure we have sufficient back-row options.
"Alex will meet up with the squad tomorrow. We've gone for him as we are still liaising with the IRB, French Federation and Castres to have Max Evans join us as soon as possible."
After facing Australia, Scotland will take on Fiji (June 16) and Samoa (June 23).
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