The trust said on Tuesday the emergency department at the QMC was designed to treat 350 patients a day, but the site was "regularly" seeing more than 500 patients.
Buckle suffered a dog bite and rang the NHS 111 service. She was then advised to go to A&E to get a tetanus jab and for someone to assess the wound.
She said she had heard about the critical incident at the hospital before being told to go there.
The 38-year-old added she was seen relatively quickly as she turned up bleeding.
"I was quite resistant to going because I knew how busy it was going to be but they said that was my best course of action," she said.
"I was told that I had to go and not risk losing my finger, so I was apprehensive."