It is illegal to be gay in Qatar. Sexual activity between people of the same sex is criminalized and can lead to serious consequences. It is not safe to be openly gay or lesbian, or to be trans.
This is why FIFA’s decision to hold the World Cup in Qatar was so heavily criticized across the world.
If you are gay, lesbian, trans, or otherwise don’t conform to stereotypical sexual and gender norms, you might do better traveling somewhere else.
If you really want to come to Qatar, then maintain distance from your partner, do not express affection in public, and keep any romantic activity behind closed doors where only the two of you can see it.
While I dislike even expressing such advice, when it comes to the Middle East, this is for your own safety.