In a word, no.
Nobody has claimed responsibility for this. Terrorists want everyone to know that they are the ones doing it so they gain the most emotional impact for their buck.
It's not their style. They prefer attacking targets that are representative of the U.S. not the American people. I'm sure this isn't getting much news time anywhere else in the world other than here. Those guys live on publicity.
FWIW, here's my amateur profile on the shooter. White male, between ages of 27-35, prior military service, general or bad conduct discharge, fascination with firearms and serial killers. Possibly married at one time, if he was it failed miserably. Single, no close attachments, loner type. Normal features, short haircut, one possibly two, military type tattoos. High school education, little if any college. No really marketable trade skills. One thing he isn't is middle eastern. Write it down.
I'll bet you any amount of money you want to bet that he's not middle eastern.
Since the topic is Al-Qaeda, I think it would be better to ask "is Al-Qaeda quick to claim responsibility for terrorism?" The answer is no. So far, Al-Qaeda's pattern is to make a vague threat, which after a little while is followed by some action which appears, in a rough and ambiguous way, to fulfill the threat. Only slowly does it come out that they did it, the better to (a)mess with or heads, and (b), get the judicial purists (Carter, Gore, Annan and half of Europe)to argue against counter-action because we don't have "incontrovertible proof."
I am not at all convinced this is Al-Qaeda, but it is foolish to rule them out, given AQ's emphasis on small arms training, including how to use small arms for terroristic purposes.