"Top" marks!

It would probably be a good idea to give it a coat of diluted 50/50 pva (white) glue. This will stop all the adhesive being absorbed into the paper mache rather than the fabric you are trying to stick on it.

If this project only needs to last through Halloween and you have a hot glue gun then I see no reason to seal it.  Spend that precious time on other parts of your costume.  Hurry up, it's already Oct 4!

In that case...
I seal my stuff with straight white glue.  Brush it on like paint.  Some people use diluted white glue (50 glue/50 water).  But in my experience, diluted white glue causes the paper to swell and potentially deform or get wavy.  Plus it doesn't dry as fast.  You can get a gallon of Elmer's white glue at Home Depot or Lowe's for about $10.  Some craft stores will sell generic brands for a few dollars less.

White PVA glue is can be water-resistant, but it's not waterPROOF.  If exposed to rain or high humidity, it tends to soften and turn whitish.

Jackie from here at the forum did some experiments and found marine varnish works best for stuff exposed to weather, but it's expensive.  For something like your hat that just might be outdoors for a short time, maybe some regular varnish from a spray can would be okay.  Since you're covering it with fabric, I would go with the matte finish.

Sue