Well, you've asked a question that isn't very easy to solve.
First of all, you've asked for a complete balanced reaction, but you give only vague suggestions regarding one of the reactants. That makes the problem a little difficult. We sometimes do try to work this way, if we know most oif the products and reactants, maybe to figure out what the formula of a reactant is.
Secondly, your reactants and products have to make sense, and your product doesn't. It isn't charge balanced -- there aren't enough bromines to account for the charge of aluminum.
Unfortunately, just because you balance the charge, still doesn't mean the compound exits, and in the case of aluminum bromide, the di- or tri- bromide don't. Instead the dialuminum hexabromide is what exists:
http://en.wikipedia.org/wiki/Aluminium_bromide