Answer: al-Qaeda or Al-Qaeda?

"Al" is the definite article in Arabic. Conventionally in Semitic languages, the article is written as part of the word with which it is associated, with no hyphen or spacing intervening (e.g., alqaeda). However, the word would be properly alphabetized without the article. The usage of a hyphen and lower case article when transliterating (e.g., al-Qaeda) is the most common form, but there there isn't really a right or wrong answer, so long as you are consistent.

If the press you are writing for uses a particular style manual, this topic will likely be covered, and you should follow its guidance.

This can further be supported with a tidbit from this Website:

"Capitalisation: capitalisation of "bin" in Arabic names would logically follow in-house capitalisation rules for "von" (German) or "du" (French). Logically, "abu" and "abd al-" require the same treatment as "bin"."

There is also a good discussion on Wikipedia regarding the transliteration of al-Qaeda.