Bicycle Mechanics - fork/headset shaky...

Hi,
I wanted to overhaul the headset of my old roadbike. Upon "opening" everything I discovered that the fork crown (the piece where the ball bearings "roll" on) is not tight, maybe 1 mm play. I put it all back together and had it tight and no shaking, etc. After driving a little bit I tested by pulling the brakes and seeing if there is any play and there was.
Could it be that 1 mm play is the cause?
If so can I get a new fork crown that is more tight or is the problem the fork, near the crown....
Thanks for any advice.
Ibo

Pictures would, as usual, help. It sounds as though the headset loosened up over the years. Overhaul the headset and replace the ball-bearings with fresh grade-25 balls. Apply grease and carefully tighten it back together. If, after you have tightened the bolts and top-nut, it is still loose, I would look into getting it a spacer to add to the stack. A trip, with the bike, to your LBS might be a good move if you've limited experience with headsets. And most shops have a bucket of spacers for your headset somewhere.

I'm betting it just needs an overhaul and careful reassembly.

I will assume you mean the crown race is loose around the fork crown.
It should be quite snug, no play. 1mm of play makes me suspect you have a 27mm JIS race on a 26.4mm ISO fork crown. But if the headset is all OEM on your bike, this would seem odd.
Don't ride the bike in its condition or you'll wreck the fork, the headset, and maybe the headtube.
Inspect the race for cracks.
Pics would be useful here to help diagnose your problem.