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I am fond of Gyrinx, so I propose experimantal 40k rules loosely based on Rogue Trader and Creature Feature rules.
Background:
A Gyrinx resembles a large cat, with very thick and fluffy ginger or orange fur and bright blue eyes. They can grow to as much as a metre in length. Gyrinx are not intelligent as such, but they have an astounding ability to empathize with other creatures, forming a mental bond with their owner which is comparable to true friendship. This mental empathy is of great benefit to the creature's owner, whose own speed of thought and action are actually improved while the Gyrinx is in close proximity. What benefit the Gyrinx obtains from the relationship is unclear, but there is plainly some deep-seated need being fulfilled, because an owner-less Gyrinx will actively seek out and adopt another creature. Oddly enough, Gyrinx show a slow metabolic change so that they can come to resemble their owner physically, temperamentally and in habit.
If a Gyrinx's owner dies, it will defend the body, and eventually either run away or allow itself to be adopted by one of its former owner's friends or associates. It takes a period of several weeks to establish a complete relationship with the new owner, but might be less if the old and new owners were close friends or relations.
Gyrinx in games are a very useful means of making powerful characters more so. Obviously, these are creatures of great value, and unlikely to be owned by ordinary people. Gyrinx are highly prized as pets by psychic Inquisitors, Rogue Traders and high-ranking members of the Adeptus Terra, etc. Even evil aliens might own Gyrinx - the creatures inherit their morality from their owner so they can be pretty mean!

GYRINX - 18 points
WS BS S T W I A Ld Sv
3 0 3 2 1 5 1 * 6+
* - as owner's Leadership or 7

Unit type: Infantry
Wargear: none
Options: Gyrinx is itself an option for its master. It can be used with either Eldar Farseer, Imperial Guard Primaris Psyker or Inquisitor with psychic powers

Special Rules
Fleet of Foot (Eldar only)

Psychic Enhance
Whilst Gyrinx is alive, its master can use an addidtional psychic power

Psychic Bond
Whilst a Gyrinx is alive, it takes wounds from Warp Perils with its master

Look out - MEEEOOOW!!! (from IG 5ed Codex)
Whilst a Gyrinx is alive, up to 2 hits allocated to the master are resolved against the Gyrinx.

...You know, I like this guy. It's somewhat underpriced, even with the reduced statline the psychic boosts make it a lot better than a Bodyguard, but make it 25 or 30pts and it's a pretty good idea.

Also, how does Psychic Bond interact with a Farseer's Ghosthelm?

Maybe it's worth 25 points.
As for the Ghosthelm, Farseer is the caster, not the Gyrinx, so the cat can't get Warp Perils damage if Farseer isn't damaged. So Gyrinx'll simply catch Warp Perils that weren't repelled by Ghosthelm.

I must get a gyrinx for my Farseers...

Oddly enough, gyrinxes already have rules. See Imperial Armor 11.