Here is an excerpt of a site that gives you instructions about medication when moving to Qatar.

Many medicines are available from pharmacies without prescription, including some that require a prescription in most western countries (although antibiotics can no longer be bought over the counter). On the other hand, some medicines that can be bought without prescription in other countries require one in Qatar and you should check with a doctor. Most pharmacies also carry non-medical items, such as cosmetics and perfumes, but costs are likely to be higher than at other shops. General medicines, such as painkillers, cough medicine and eye drops, are widely available in supermarkets and larger stores.

Note, however, that Health Ministry in Qatar has banned the use of tranquillisers, anti-depressants and in some instances sleeping pills, except for extreme cases associated with certain types of mental illness. (Ministers have seen the problems caused by their overuse in the west.) If you’re dependent on any of these medicines and carry them with you, you must ensure that you’re also carrying the doctor’s prescription and preferably a letter from your doctor confirming that you need them. You’re most unlikely to be able to obtain new supplies when in Qatar, so have enough for your requirements, but not so many that you could be suspected of carrying drugs for sale.

If you take a medicine on a regular basis, make sure that you know the content name and formula, not just the brand name, as many brand names vary from country to country and between manufacturers. You might have to renew your prescription from a local doctor, as many pharmacists aren’t authorised to accept foreign prescriptions.