I carried the kitten home on the tube in a shoebox. I was living with my parents while I looked for a flat with my new boyfriend, who lived above a fish smokers – it was no place for cats. We called her Edie after Edith Massey who played the Egg Lady in Pink Flamingos, a woman who, John Waters remembered, was a nightmare on car journeys because she would name everything she saw: “Tree! Cow! Squirrel!� When I moved out, Edie stayed with my parents for a life of gardens, and scallops for tea.

Ten years later, I held her tightly as my mum showed me how to put on a nappy, having first cut a hole out for the tail. It was a month before my boyfriend and I had a daughter, whose first word, of course, was Edie. When she toddled towards the cushion by the radiator, again and again, Edie would do the cat’s version of rolling her eyes, looking at me with grand disgust as the kid stroked her wrong. “Edie is my best friend,� my daughter would say, hugging her too tight.

Two weeks ago, my mum noticed a lump on Edie’s hip. The next day it was as big as a mouse. Her leg swelled, her paw looked obscene, and the vet said there was nothing we could do.

Our daughter noticed a tone change at teatime. At home, all her toys became ill in an afternoon, and our flat took on the biscuity scent of a hospital as she cheerily administered opium to Puppy, his batteries removed. So this week we’ve been working out how to tell a two-year-old that death exists.

The problem is, there are three problems. First, she is so new to language that midway through a monologue about cake, she will delightedly announce how good she is at talking now, thereby breaking the fourth wall of conversation and making you consider the filminess of words.

Second, every explanation leads to four or five more. We talked about animals getting very tired, and one day not waking up. Which led to a sudden fear of going to bed. My mum phoned me at work. “I’m panicking – I’ve started telling her about heaven?� We agreed, heaven was a nice idea, but a bit… bollocks. We talked about getting ill, which was confusing in the context of Calpol, and we talked about getting old, which led to the third problem.

This has become about more than a cat. A great cat, sure – a noble, lazy, affectionate cat with a proud low-hanging belly that my mum folds under when carrying her in company. But more, too. After a week of documenting the end of Edie, yesterday I took a photo of my daughter curled under my mum’s arm as she read her a story. And with humour darker than soil, my mum raised her eyebrows saying: “We know what photos are for.�

There is a gloomy existential cloud over every interaction as Edie gets thinner, unexpectedly no longer a kitten. Death exists. On Friday it did that cruel trick it sometimes does, too, where the dying subject seems suddenly cured. Edie became briefly ravenous, and leant into every stroke, purring noisily. The vet said: “She’s a cat, purring is what they do,� which made me hate her. For a second I thought we had dodged it, but no, death still waits in every conversational crack. You pick up a picture book, or a plate, and there it is again.

At two, my child is connecting the pieces of the world like Lego. We see a lost cat poster, and she suggests we make one for Edie. Going to bed one night, she tells me Edie is going to fly off into the sky. It’s only later, in the dark, that we realise she has gathered this, not from our fumbled attempts at explaining the cruelty of nature, but from Raymond Briggs. The Snowman is one, The Bear is another – books that end with a beloved best friend padding away across the garden and into the night sky, inevitable and gone.

Later we’re buying a helium balloon, so she can watch something fly away. When I finish this sentence, I’ll file to my editor, then walk round to say goodbye to Edie, whose painkillers ran out this morning, and who has an appointment at the vet after lunch. One more sentence. OK.

Email Eva at e.wiseman@observer.co.uk or follow her on Twitter @EvaWiseman