Another way of reading the specs is:
It must start (yup, ^ will do)
with a letter (yup, [a-zA-Z] is the way to go),
followed by 2 to 7 letters or digits (check out {m,n}),
followed by the end of the string (\z).

You don't even need to call length.

By the way, enclose code in <c>...</c> tags on PerlMonks. It'll handle formatting and escaping characters such as &<>[] for you.

Update: I wrote "0 to 7 letters or digits" where I meant to write "2 to 7 letters or digits". Fixed. (Maybe I was checking if you were paying attention ;) )