First of all, let's define laughable. Summarising from several dictionaries, one can say it refers to something that makes you laugh because:
a) it's amusing (which seems to imply something pleasant, comical, entertaining)
b) it's absurd
Now let me pick up the given example: intelligent rabbits are invading.
This example plays the absurd line: everyone knows rabbits are small animals with a high level of cuteness but low intelligence that reproduce quickly in order to survive a world where everyone eats them (a pity that cuteness doesn't deter predators). They're physically harmless to bigger, hardier creatures.
The absurdity stems from the wide gap separating the well-known reality - cute harmless creature - from the uncommon fictional reality - a capable invader (which implies intelligence, big muscles, and... well, big bodies). After all, films have given us intelligent sharks (and other animals I fail to remember) and the absurdity stemmed mostly from the plot and the humans' actions, because the threat the sharks presented was relatively legit.
The Gremlins come to mind too. For as long as they're cute little furballs, they're harmless. Once they lose their fur and become scaly, toothy monstruous looking critters, then their level of threat can be taken seriously (and this was a comedy).
Bottom line: an appearance describable as small, cute and harmless cannot be taken seriously and becomes laughable when presented as a threat.
What one must keep in mind, however, is that small, cute and harmless only come together within the reader's notions! It's basically a prejudice: if a creature is small and cute, surely it can do no harm. Just look at koalas! They're like big, sweet teddy bears, right? Except one should avoid getting too close as they have a vicious bite. And bunnies themselves! Through the 19th century and the first half of the 20th century, bunnies were not seen as cute and harmless in Australia. They were a pest that cyclically made the headlines as plagues swept the country.
Perhaps the reader is 'prejudiced' and thinks of cute harmlessness at the sound of the word 'bunny'. What about the fantasy world inhabitants? I'm pretty sure 'bunny' for them would be, in the very least, the equivalent of 'rat' for the reader.
How to set it up?
Let's say one wants to go all the way and use the word 'bunny' coupled with the actual visual of our real life rabbits.
First of all, why are they a threat? Surely it isn't because they're super-strong axe-wielding warriors. Because we're keeping their biology intact, they can't even create tools since their paws don't allow it.
1) They have developped intelligence and their aim is to create large areas that are predator free.
2) As their numbers grow, they will spread out. Despite their intelligence, they haven't yet realised that the world is finite and they will one day have nowhere else to move to (big surprise: how many milennia did humans take to realise it?).
3) They do have a culture, that varies across the different communities. They have different languages and art (they carve trees using their teeth). It looks like random chewed stuff to humanoid races, but the bunnies are aware of how delicate and deep such works are.
4) They have two classes of enemies: irrational predators (like foxes and eagles) and rational predators (humans, elves, etc).
4a) The irrational predators are dealt with through traps, guerrilla techniques and a sort of 'pavlov reflex' (if the predators can learn that bunnies does not equal certain lunch, they'll prefer easier prey).
4b) Rational predators are a two fold danger: they do not only hunt and kill bunnies, but their towns and fields also encroach in what the bunnies consider to be their ideal environment.
They have developed specific fighting techniques to face them: to undermine their food source (only the best warriors - fast and experts at hiding), they destroy their crops and kill their cattle. They have learnt to use specific poisonous plants which they chew just before biting the animals, with the poison spreading through their blood system. Only a specific warrior class goes through the training to become immune to these poisons. If the humanoids use water pipes, they will be gnawed and poison will be added to it.
To use the same poisoning technique in the humanoids is tricky, but it's still widely used with solitary individuals. Their biggest advantage was that the humanoids had no idea where the danger lay, but, unfortunately, the elves have figured it out. Fortunately, orcs and humans still underestimate their abilities.
In the meantime, their most intelligent members are working on ways to transmit the humanoids a disease which will prove deadly to them, while inconsequential to the bunnies.
In the story
Now the world building is done, let's focus on the writing. The trick is to make sure the reader only sees the word bunny in association with how negative they are. Soon, even the reader will shudder at the thought of bunnies.
"Weirian, we must rally everyone: I've come across bunny markings."
"Are you certain?"
"Yes. Right next to the well, and you know what that means: poisoned water. I've already sent my wife and children to my sister's. They live further from the fields."
Weirian closed his fists tight. A single bunny had once burrowed into his house, three years ago, then bitten his young child with their poison. They were small and discrete, and had been known to kill whole sleeping families. Weirian lived to eradicate those monsters.
What turns something laughable into credible is... making the threat credible. Think up the least threatening creature (or individual) at first sight, then focus on the world-building part and give them something that makes them truly dangerous. Going with a (mildly) realistic threat is probably better. One already has to suspend disbelief to see the bunnies (or whatever) as threatening, so make sure the rest isn't too far-fetched.