If we nurtured them as members of the family, she points out, bilbies and quolls wouldn't be endangered.

Her sister, Lucy Culliton, agrees, although for her, all animals are equal, from the cows, horses and sheep she's gathered on her property on the Monaro, to the cockatiels that fly around her living room and greyhounds that nestle in her armchairs.

The sisters – Lucy a painter and Anna a ceramicist – have long incorporated animals into their work, informed largely by their love of the land and respective country lifestyles, although both insist that their work isn't about country life at all.

For them, "country" denotes farming, livestock, slaughter houses.

"It's not really about country, because we're both vegetarian!" says Lucy.

But both live on large blocks of land outside the city, and both pursue themes in their work that evoke the pastoral, and a deep connection to animals, both wild and domestic.

It's a sunny Tuesday morning and we're having coffee in the garden at Beaver Galleries in Deakin, where the sisters have their first ever joint show, Our Animals, a celebration of the connection between humans and animals, and the love they have for the living creatures that share their space every day.

From the walls, Lucy's sheep, painted in oils, peer solemnly – straight-on, portrait style and full of character – and baby chicks are captured mid-strut. A group of cows are placed, painterly and serene, in a formal group, while a white rabbit peeks shyly at the viewer, one ear flopping endearingly downward.

And, scattered throughout are Anna's intricate ceramics – flowers and fruit in bright glazed porcelain – with tiny native animals sniffing about. A sugar glider here, a delicate grey shrike thrush, called Meadow, there. They're inspired not by pets, but by the animals that live around her.

The sisters grew up with lots of animals – living in Hornsby in Sydney, they had plenty of pets, and at one point, their mother instructed the local pet shop to stop selling Lucy pets without her permission.

"I used to spend money on a mouse or a bird or a fish," she says.

They also brought home injured animals on a regular basis, of the "squashed half-dead blue-tongue" variety, and their parents encouraged their nurturing side.

It's an impulse that's never gone away; it's worth pointing out that as we speak, Anna is cradling Josie, a baby wombat she rescued from her dead mother's pouch by the side of the road. Out in the car, with Anna's sleeping husband, is another rescue, this time a joey, along with a sleek greyhound.

Baby Josie, with her flat brown nose and curled up claws, was star of the show two weeks ago at the National Portrait Gallery, when Anna smuggled her in to the opening of The Popular Pet Show, the gallery's summer blockbuster (despite a strict No Living Animals policy at the launch, Josie is on a carefully monitored diet of – wait for it – wombat formula, and can't be left alone). The sisters are both featured in the vast, joyful exhibition, alongside 13 other contemporary Australian artists, and this smaller show at Beaver is something of a companion exhibition.

Lucy, an established artist who trained at the National Art School is a regular finalist in the Archibald, Wynne and Sulman Prizes at the Art Gallery of NSW, has recently been taken on a Beaver Galleries, after her gallerist of 20 years, Ray Hughes, retired.

Anna, on the other hand, is a self-taught potter – the only ceramicist in the Portrait Gallery show – who never planned to become a full-time artist, but now, after exhibiting regularly since the mid-2000s, most certainly is.

Both work from home studios on large properties; the pair once shared a damp, dark terrace on Crown Street in Surrey Hills – bought in the 1980s, back when it was "Scummy Hills". When their parents retired to the Kanimbla Valley west of the Blue Mountains, Anna and her family moved nearby not long after. Lucy worked from a studio on the property, before selling the Surrey Hills house and moving six hours north of Kanimbla to Bibbenluke on the Monaro in 2008.

Until this year, Anna says she wasn't ready to show her work alongside Lucy's.

"I haven't been in Lucy's league by any standard, and even now I feel a little bit overwhelmed," she says.

But the two have such similar outlooks it seems incredible that a joint show is a relatively new concept.

"I always try to put an animal into something, only because the relationship between people and animals is so important," says Anna.

"And I've done a circus theme - it has to have animals, and a rodeo theme has to have animals."

Lucy, meanwhile, tends to work in phases, sweeping themes that last years. Landscapes, then her five-acre garden, then flowers, then flowers in glass bottles. She's now on a mission to depict every one of her animals – all pets, all rescued, all kept out of habit. But her partner recently informed her that she'd reached something of a limit, hence the decision to capture them all on canvas.

She's also been on a country show track – one series included paintings of crocheted coat hangers, chocolate cakes, dolls in crocheted baby outfits.

"Pikelets. I had six paintings of pikelets," she says.

So, no country theme, then?

"I'm pretty country," Lucy admits.

"As soon as I moved out of home into Surrey Hills, I kept horses in the showground. So I always had an animal connection. Not that I like the country - I don't like country, I hate live export, I hate killing animals, all that grain that we feed to the cows should be fed to the people."

Then again, the sisters have another joint show coming up in Tamworth, Anna once had a fixation on cowboys and rodeo in her art, and says the shrike thrush in her work –the real one called Meadow – actually lives in a nest by her front door.

"We call her our life coach because she just stops you slamming the door, and she just makes everybody calm," she says.

"And the coats at the front door, you can't wear because there's bats in the pockets, so you just leave them there. They just move in."

Okay, they are pretty country then. Lucy even admits, grudgingly, that she does have a bit of a country house theme in her home – cushions with horses on them and the like – although that's mainly because people keep giving them to her.

Ultimately, they hope people will get a sense of joy from their exhibition, or, at the very least, learn to appreciate their own animals more.

"I hope they go home and pat their dogs," says Lucy.

Our Animals, by Lucy Culliton and Anna Culliton is showing at Beaver Galleries until November 27.