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Not yet. Oman Air has applied for membership in Oneworld, which will grant top tier Oman Air frequent flyers access to lounges on Oneworld partner airlines including Qatar, but the process is not expected to be completed until 2024.
Oman Air does already have a code share agreement with Qatar, so you may have access to the lounges that Oman Air uses if and only if you booked with Oman Air flight numbers (WY). But if your booking has Qatar flight numbers (QR), you're out of luck.