I haven't used VEVO but my understanding is it is how you check your visa status with the Australian government. Is that right?
If the official government website can't find your visa, yes, you have reason to worry. The airport staff can't be counted on to fix anything. I would call the immigration office in Australia ASAP. You might not be able to find any working numbers as it will be the weekend. Try to check on your visa another way, if possible.
If you can't get anywhere, then just print out a hard copy of your 600 visa details. Don't bother the check-in agent with any questions about VEVO or imply there are any problems with your visa. Just show them the paperwork. That may be enough to check-in. Then once you arrive to Australia, hopefully you can sort out any technical problems directly. I suspect there is a simple error that can be sorted out in Australia, but your greatest issue would be denied boarding. So just be prepared to show your visa details to the check-in agent.