Definitely bake it before freezing it. If you can wait until closer to the event (two weeks or so), I would, but it'll definitely be fine for a month in the freezer.

I''ve had good results both ways (freezing baked or unnamed). My notes say cooked pudding freezes well for up to 2 months, uncooked for one month. so you pays your money and you takes yer choice. Just don't reheat baked frozen defrosted pudding in microwave.

Now that's planning! And technically, June is merely 2 weeks away. I frequently have individual bread puddings left over from large banquets, and yes, bake first, then wrap in two layers of plastic. Thaw in the refrigerator overnight. Bring to room temp for a half hour or so, then reheat in the oven for 10-15 minutes. If you are making one bulk bake, bring it to room temp for an hour, and reheat for 20-25 minutes, depending upon how deep it is. Seriously, I admire your ability to plan so systematically ahead.

I would definitely bake and then freeze. Make sure the pudding is cool before wrapping it tightly in two layers of plastic wrap and freezing it.