Taken from Gov.uk website:
Relationships outside of marriage
Any intimacy in public between men and women (including between teenagers) can lead to arrest.
Living together whilst unmarried is prohibited in Qatar, and sex outside of marriage, regardless of whether this is same sex couples or opposite sex couples, is illegal. This can lead to arrest and a potential court case where the judgement can include a fine, a custodial sentence and deportation once the sentence is complete. This is especially so where the behaviour has caused offence. See Local laws and customs page.
Due to the laws on sex outside marriage, if you become pregnant outside marriage, both you and your partner could face imprisonment and/or deportation. Doctors will ask for proof of marriage during ante-natal checks. An unmarried woman who gives birth in Qatar may also encounter problems when registering the birth of the child in Qatar, and could be arrested, imprisoned or deported. To get a birth certificate from the Qatari authorities, you must provide a marriage certificate and the authorities may compare the date of the marriage against the estimated date of conception.
There are also very strict rules regarding alcohol, dress code etc.,
Why not look at Dubai instead?