Luna the labrador was 10 years old when Watson couple Liz Friend and Chris Whitlock took her home.
The pair "accidentally" adopted Luna from a labrador rescue last year.
"We weren't looking for a dog because we already have two other dogs at home, it kind of just happened," Ms Friend said.
"But when we saw her we thought, 'Oh my god, that poor dog'."
Luna was born deaf and diagnosed with a neurological problem, likely caused by a brain tumour. The now 11-year-old also had anxiety and other problems, too.
"But it wasn't really affecting her life and she was on some special food to help her brain and she was on lots of medication for lots of other things like arthritis," she said.
"Since we got her, we've fixed her up and she was going really well."
But on Christmas day Luna was rushed to the vet after a seizure.
"She sort of didn't recover from them and then suddenly couldn't walk properly," she said.
"It all happened so quick, only a couple of days ago she had been a normal dog, running around and playing with our other dogs, Ron and Nynaeve."
They were told they would only have a few more days with Luna. The labrador was to be put to sleep on Wednesday.
"She likes to run around and stuff so it was really sad to see that she just couldn't get around. I just thought if we popped her in a little trolley that she could still come for a walk."
On Sunday, the pair posted a Gumtree advertisement in search for a "cart for a senior dog to go for a walk".
The post read: "My old girl Luna is very vey sick and is going to have to be put to sleep in a few days. She can't walk anymore and I want to take her to the park one more time so I desperately need a cart like the one above for her to lay in so she can go out and about again.
"We won't need it for very long, only a few days, and can give it back if you don't want to part with it."
Within hours, the pair was inundated with messages of support.
"So many people rang me just to say that they were sorry to hear. We had people calling and saying that they didn't have a cart but would ask around," she said.
They pair were not able to get a second-hand cart, but after recommendations bought one from Bunnings.
On Monday morning, Ms Friend and Mr Whitlock took Luna for a walk around Lake Burley Griffin.
"Nowadays she's just asleep on the couch which is what she was doing all day, everyday when she was sick but as soon as we put her in the trolley and took her out she had her head up and was looking around and wagging her tail," she said.
"She really liked it, really liked going out and loved the people looking at her."
Mr Whitlock said even though they knew they wouldn't have her for long, they were happy with how far she had grown.
"She was a very anxious dog, but was the friendliest dog though, the most gentle thing. She would just sit by you on your lap and she's just super people friendly," he said.