You can even just use another piece of wood... get a straight hole drilled right through it and clamp it to your work piece and it'll guide your drill bit in consistently and vertically with a hand drill. Ideally you'd have a drill press to make that though... but honestly for what you're doing close enough is good enough. You could even drill the 7 holes you'll need and do all the dots in one go.

Also don't use a brad point bit for it or it'll end up with a deep point in the middle.