All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad, sallallaahu ‘alayhi wa sallam, is His slave and messenger.
A poor person is an eligible recipient of Zakah. According to Muslim scholars, the criterion for considering a person as needy is that he earns an amount of money that is not enough for his food, drink and clothing and other things that he needs for himself and for those whom he is ordered to provide for in the Sharee'ah. For example, if someone needs 10,000 but he only has 7,000 or 8,000, such a person may be given enough of the Zakah to complement his need. Therefore, if the salary of your brother is, as you mentioned, not enough for him and he does not have another source of income, then it is permissible for you to give your Zakah to complements his needs.
However, if your brother is living in Qatar - as the data in the question indicate that he lives in Qatar – then the salary which you mentioned in the question (13,000 QR) is enough for the need of a man, his wife and his daughter. So, in our view he is not included among the needy people. But if the payment of his debt is due and he is unable to repay it, then it is permissible for you to give your Zakah to him, because he is in debt, and the indebted person is among the people who are eligible for Zakah. Nonetheless, if his debt is not immediately due, then the scholars differed in opinion regarding paying Zakah to an indebted person whose debt is not immediate. Some scholars say that it is permissible to pay Zakah to such a person, while others say that it is not permissible. A third view suggests that if his debt is due in that year, it is permissible to give Zakah to him, otherwise it is not. Imaam An-Nawawi is of the opinion that the correct view is that in such a case the person is not given Zakah [he is not eligible for it].
In case he is entitled to Zakah [according to what we have explained above], then you are not obliged to inform him that the money that you give to him is Zakah money. An-Nawawi said (in Al-Majmoo'): “When the money owner or any other person [as when he entrusts another person to do this on his behalf], pays Zakah to a person who is entitled to it, and he does not inform him that it is Zakah money, or does not say anything at all, then this is a valid fulfillment of the obligation and takes effect as Zakah…..” [End of quote]
On the other hand, Ibn Qudaamah said in Al-Mughni: “If one pays Zakah to a person whom he believes to be poor, he does not need to inform him that it is Zakah. Al-Hasan said: 'Do you want to embarrass him, do not tell him.' Besides, Ahmad ibn Al-Hasan said: I said to Ahmad: 'When a man gives Zakah to another should he inform him that it is Zakah money, or should he be silent?' He [Ahmad] said: 'Why should he embarrass him with such a statement; he should give him, and not inform him; he does not need to embarrass him.” [End of quote] For more benefit, please refer to Fatwa 85173.
However, if one knows that the person to whom he wants to pay Zakah does not accept Zakah money, then it is an obligation to inform him, because one should not make him possess against his consent. Shaykh Al-‘Uthaymeen said: “If a person gives Zakah to someone who is eligible for it, then if this person who is eligible for Zakah refuses Zakah and does not accept it, then the owner of the money must inform him that it is Zakah money. Thus, he would know the matter and then he can take it if he so wishes, or refuse to take it if he so wishes. However, if one usually takes Zakah money, then one (i.e. the giver of Zakah) should not inform him, because informing him that it is Zakah money is a kind of reminder of favors. Allaah says (what means): {O you who have believed, do not invalidate your charities with reminders [of it] or injury.} [Quran 2:264].” [End of quote]
In case you pay Zakah to your brother and he gives it back to you, then you should give it to any other person who is entitled to receive Zakah.
For more information, please refer to Fatwa 81297.
Allaah Knows best.