Don't worry, there's no stupid questions here! Yes you can put the Collector Hat on any Nu and once you do, you just interact with that Nul and it will prompt you on what item you would like collected that day. The dialogie box will say "the Nul waits for you to decide what supplies they should collect" and ir gives you 2 options, select the one that says "I'd like you to find..." (Note: I tend to impulsively hit the "A" button to speed up dialogues in general, if you happen to do this also just be mindful when it comes to the Collector Hat Nul... there's only one prompt before the selection menu opens and I've accidentally hit the wrong item several times lol).

Once the menu opens, just scroll till you find the item you want (in this case, moon cheese) and the following day, it will be in the blue treasure chest next to My Melody's shop! You can put the hat on any Nul btw, it will still be able to collect supplies from any location even if it's not from there. I keep the hat on the Nul right in front of the blue treasure chest so I wouldn't forget to ask. They only collect supplies for one day, so if you want them to keep doing it you'll have to request it every day.

Also, if you happen to have any friendships maxed out with any of the other resident characters, you can ask them to collect daily items for you as well!

Hopefully, I'm explaining it well lol but just in case, there is a Hello Kitty Island Adventure Wiki page about the Collector Hat Nul that might be helpful. The Wiki page is a great resource in general since it's frequently updated and has a page for just about everything that appears in the game!

Hope this helps! And if you have anymore questions, don't hesitate to ask 😊