That sounds like such a sweet idea and a very special birthday for your little Moomin! I love how many of us have our own Moomin connections; it really shows how beloved these characters are across generations.
For cupcake cases, I’ve noticed that Moomin-themed baking supplies can be a bit tricky to find depending on where you’re based. If you’re open to getting creative, one idea is to use plain pastel or nature-themed cases and then top them with Moomin-inspired decorations. I recently used this lovely website for a forest-themed party, they have charming ceramic cake toppers (including animals and woodland motifs) that could pair beautifully with a Moomin vibe. Not officially branded, but they definitely have that whimsical, storybook feel.
Also, Etsy might be worth a look there are often small batch creators with themed cupcake wraps or printable toppers. Hope that helps, and I’d love to see how the cake turns out!