My first bunny Bandit was around 4 when we got our cat Nikko from my uncles who found her in a park in NYC. They were allergic to cats so couldn’t keep her so we took her in. She was almost fully grown (past 6 months under a year). As such she was energetic but not overly so and she had decent control of her strength. She was also old enough to learn things and retain them.
Bandit our dwarf hotot mix was a very confident bunny and didn’t mind playing with her. Sometimes they’d lie in the sun near each other after chasing each other around (she’d chase him, then they’d reverse and he’d chase her). Other times she would sleep in a chair and he’d sleep directly underneath it. He helped teach our cat not to view bunnies as prey. (Mice are fair game though, she somehow always finds them even as an indoor only cat...)
Nikko is now 17-18 and our current bunny Minyeong (now 1) gets along with her great. He follows her around which she tolerates and she bats him on the head with a soft paw (no claws extended though she easily could) when he goes too far. She’s too old to want to play with him though even when he tries. Even when we got this netherland dwarf bunny at 8 weeks he was a confident rabbit.
One thing you need to make sure of is that your bunny is self-confident. A confident rabbit will have an easier time meeting other animals. When it comes to a cat (just like with the bunny) personality is a big factor. If you go with an older cat, you may be able to adopt one that has a known mild temperament and a low prey drive. If you want to go with a young, be extremely watchful. Kittens do not know their own strength and can be extremely rough. When cats get between 6months to a year like our cat when we first got her, they are still playful but are more impressionable which could be a good time to establish that bunnies are “friends” not prey.