Whether or not you have saved enough should be a function of living expenses, not wages.
If you have $5k and can live on $600/month, that's great. If you need $1k/month in expenses, then it's not great at all.
As soon as possible, you need to have enough saved to cover an unexpected, large expense (car/home repair, medical emergency, moving to a new place, etc.) and at least 6 months of living expenses. I personally have at least 12 months of living expenses at any given time.