Praise be to Allaah.
Your maternal uncle’s daughter is not counted as one of your mahrams, so the same rulings apply to her as to other women who are “strangers” to you (i.e., non-mahrams). One of these rulings is that it is permissible for you to marry her. But we should note an important point, which is that even though love is something nice, and it is mustahabb for a man to marry a woman whom he loves, because the Prophet (peace and blessings of Allaah be upon him) said: “there is nothing better for two who love one another than marriage” (Saheeh al-Jaami’, no 5200), nevertheless, this love should not be overwhelming and cause a person to forget other characteristics which he should look for in the person he wants to marry. The most important characteristic is religious commitment. The Prophet (peace and blessings of Allaah be upon him) said: “A woman may be married for four things – her wealth, her lineage, her beauty and her commitment to religion. Choose the one who is religious, may your hands be rubbed with dust [i.e., may you prosper]!” (Agreed upon). If your cousin is religious and has a good attitude, then you have chosen well and we ask Allaah to fulfil your hopes and bring you together in a good way. If she is not, then think again about your choice. May Allaah help you to do that which He loves and which pleases Him.
Sheikh Muhammed Salih Al-Munajjid