I agree with the two users above, it'll take ages to get enough. But, it is doable! It's my current goal rn.
If you're any good at art, I recommend trying to make some custom apparel - it costs 100 ms to submit it, but then you get 5 copies of each, all of which you can sell for pretty good prices. You can also open an art shop on the forums - I have one right now, and so far, I've made 15 ms from it. Not a lot, but still good!
If you're okay with grinding, I'd say get and cook as much food as possible. Then, sell stacks of 99 cooked food for 1 ms on the flea market. Not the fastest way to make moonstones, but pretty good.
WWs are also a good way to make ms. Sometimes I flip WWs from the flea market (although most of the time I don't do this intentionally - I buy a wolf thinking I'll love them, but end up hating them). If you buy a WW for 1 ms, you can maybe sell it for 3-5. You can also go hunting for WWs. And, if you're not sure you're going to get anything good from a knucklebone hunt, you can sell the knucklebones for a pretty good price. My current exchange rate with the person I trade knucklebones with is 1ms:2kb. So 50 might be 25, if you get a good rate like that.
Grinding events might be good too. I haven't personally done this but I know people pay insane amounts of pebbles for event companions, so I imagine they pay in ms as well.
You can also sell pebbles, if you have enough. Right now I think the rate is 25k pebbles to 1 ms, so you could list a bunch of pebbles on the flea market and get some ms for it.
Good luck in getting the breed change!