The most common pilot job ads on afap.org.au are flying instructor positions. Many of the organisations advertising are not schools who train overseas pilots.
Grade 1 and 2 instructors are in high demand, however junior grade 3s are not in such demand.
Speak to the school you'll be training with and ask what the job prospects are after you 'graduate'. You should already have an idea about how they work and whether this is possible. It is unlikely you will have a guaranteed job at the end though.