Qatar flights tend to post on Wednesday, and then you'd be silver a day or two after that.
If the positioning flight gets you into silver status then that should be plenty of time.
KA check-in opens 48 hours in advance, so if you're still bronze at that stage, don't check in until closer to departure as your boarding pass may still show ruby status and won't update.
If the positioning flight is all you need to hit silver, you should be fine six days later.