Yes, Qatar's Penal Code applies to everyone within the country's jurisdiction, including foreign expats. Under Article 13, the law applies to any person who commits an offence within the territory of Qatar, regardless of their nationality. This means that simply being a foreign national does not exempt you from Qatari criminal law.
It is also important to know that the law can follow you even beyond Qatar's borders in certain circumstances. Article 16 extends the Penal Code's reach to anyone who commits an act outside Qatar that makes them a perpetrator or accomplice in a crime that partially or wholly takes place within Qatar. Additionally, Article 17 specifically covers serious offences like drug trafficking and human trafficking committed abroad if you subsequently reside in Qatar.
As a practical matter, expats should be aware that some provisions of the law are also governed by Islamic Shari'a principles. Article 1 notes that Shari'a provisions apply to certain offences — such as theft — when either the defendant or the plaintiff is Muslim. Always seek legal advice from a qualified Qatari lawyer if you are uncertain how a specific law applies to your situation.
This is general legal information, not legal advice. For advice on your specific situation, consult a lawyer licensed in Qatar.