Broccoli will certainly be safe, even after a whole day with no refrigeration. Maybe a little limp, but taste and nutrition-wise, it'll be fine.

White glue will hold on fabric BUT it is usually not water-safe, so if you have rain, it'll fall apart.

Bright orange fabric with black text, and I would make a "circle/slash" with a dog biscuit shape inside it. A "Vest" would probably be more effective, and more visible to people than a bandana, just to be safe. Folks are used to reading words on vests for service dogs.

Just my 2 cents!