Well, you've got the right idea, use the dowel to fill the hole, and then re-drill. While you are at though, why not replace the crappy posts and bridge with a better unit? Or at least replace the posts and anchors with better ones? Get some Edge studs and anchors, and when you have the cash (if you don't have it already), source an Edge Pro, which will fit in the route. 
If you are taking the time to do a nice re-finishing job for yourself you may as well give your guitar a better bridge that'll last you a lifetime too.
If you are taking the time to do a nice re-finishing job for yourself you may as well give your guitar a better bridge that'll last you a lifetime too.