Animals such as dogs, cats etc. became that type of being by doing various misdeeds when they were humans a long time ago. These Asathpurusha — People who did bad things — became animals to repay for the bad things they did, so they can rebalance the world.
Animals are a result of that previous human who did bad things. Therefore, you cannot end the suffering of all the Animals in the world. Nothing you do will make them back Humans, not until they've paid their debt, not until they get a Human Type from the random pool for the next life at the death.
However, there are things you CAN do to prevent more Animals from coming to the world.
How exactly? By making more people aware about the nature of reality and making them aware about Buddhism.
If you do X, Y, Z things all the time, then your next life is crafted based on what you think, do and say. If you can turn more people to do stuff that gets a Human life, that's how you stop creating more Animals.
IF you can help 1 person to attain Sowan (Sotapanna), Sakrudagami (Sakadagami), Anagami or Arihath (Arahant), that's how you prevent 1 more Animal coming to the world for FOREVER.
You think your idea of "destroying all the animals in the world with a Black Hole" isn't evil, but it is not. Not sure why? Let me explain!
No one likes to be killed. No one likes to be hurt. As such you're doing an evil thing for the Animals by killing them to save them without their explicit permission. Even if you have the permission from the Animals, you're in fact doing a misdeed by killing them. That accumulates you sins or "factors" to be born as a potential animal in the next life, guaranteed death by such situations in future lives.
Even if you killed them, they will still be reborn as Animals or as an another being which still have suffering. Because it does not matter if it's an Animal, Human, Deva or a Brahma, suffering is still there. That's why attaining Arhat stage is important.
Then the "Black Hole" is actually a Hell where Pure Delusional people are reborn who perform Anantariya Sins such as killing their biological mother or father among 6 other things.
That hell does not get destroyed even at the biggest end of the worlds. Beings there live for a Trillions of Trillion years until their debt is paid.
If you're wondering why allowing animals to suffer isn't evil, here's why.
That "Animal" was born to pay its debt accumulated by its own misdeeds when it became a Human. By allowing them to continue their course of life, you're giving them the chance to pay that debt the only way that Animal can pay it.
By not trying to change the fate of that Animal through inefficient and illogical means, you're creating a ton more Raga (Lust), Dwesha (Anger), Moha (Delusion) thoughts, actions which pollute the world. How deep is that pollution? That spreads up to 10,000 Lokha Dhatus. That means you're causing a huge chain of Negative Energy and Sins not just for you & that animal, but trillions and trillions of beings in all 31 Realms.
So as a summary, you cannot end the suffering of anyone by killing them. The only way is attaining Nibbana which prevents being born as any type of being including the Animals. Right now, you won't see this as the only way, but as you dig deeper on WHY, you'll realize it.
Good luck on your journey!