I read a post earlier about a writer wanting to have a Muslim character in their story. I would say most importantly, figure out whether you want a Muslim character or a character with an Islamic background. There are Arab Christians,Jews (as strange as that may sound) Buddhist and so on. If their religion plays an important role, then specify if they're Muslim. If not, you may not need to specify their religion at all. There are several Muslim writers who have written books about Muslims, however, the characters practice the religion out of custom or not at all. In many books its just to add diversity or do something new.
Imagine a book where the main character is said to be a Vegetarian. But he/she eats a Whopper everyday, vegetarians will most likely feel insulted and others would wonder why is this character is considered vegetarian at all. Religion encompasses not just dietary restrictions, but dress code, marriage laws, business practices, etc. Of course, if the story is about a character who has a change of faith or is struggling with following it, then that makes it more understandable for the rules to be broken. Also, if the character is really young and doesn't really care about religion, (once again, if this is so, know why you want a Muslim character in the first place)
Also, there are no perfect Muslims. (This is probably good for readers who come across Muslim characters in books, too) Culture has a lot of influence on the religion. Make sure you learn the differences between the culture and the religion, and know ahead of time, not everyone is going to be pleased with the portrayal.
Lastly, if you want to write about an Arab Muslim, go ahead, please do. But don't forget there are Native Americans, huge amounts of African Americans, Chineses, Latinos, Europeans, etc, who claim Islam as their religion.

I hope this helps someone.