Hello,
I am afraid you cannot change the default font within the notes app. You can however use third party keyboards you can download from the app store and use the fonts provided within the program. Personally, the app FancyKey Pro has always done the job for me when I wanted fancy fonts, but sadly, after checking, has been taken down by the developers. I’ll link another that might be helpful for you! While you can’t change the font, you can however change other things within a note. While the keyboard is up on your iPhone, there will be a button showing two (a)s and will look like this: “Aa”. If you press it, you can change the format a little. I’ve included some pictures for you below and a guide to using the Apple Notes app.
Using Notes on Your iPhone, iPad, and iPod Touch - Apple Support
Fonts - App Store
Sincerely,
Captain