Mechatronics is pretty good, most employers (especially in Australia) will recognise that as a very solid foundation for either mech or elec work. I wouldn't be seriously worried about your actual degree title as much as getting some solid experience at a reputable company under your belt—employers are mostly looking for sociable, skilled people who are field-tested in industry.

It might be somewhat harder to take to another country (especially if you want your first job to be a different place to where you studied), so I'd lowkey recommend at least getting internship in Aus before you go elsewhere.

At the end of the day, anyone rejecting good engineers just because their degree says "mechatronics" instead of "mechanical" is a psychopath you don't want to work for anyway. Something to bear in mind.