In Theory ( OM Part A chapter 8)
Time before being considered for upgrade:
3 years ( to count from day of final line check ) and min TT of 5000hrs heavy jet.
Time before fleet transfer:
2 years minimum ( new rule )
In real life....
QR has , as of today, 840 pilots of which +/- 450 are FOs. Currently the upgrade capacity is 4/month on A320 en 2/month on A330. (72/year)
Do the calculations yourself....But three years is VERY optimistic.
