"I noticed straight away it didn’t taste like my normal chocolate," she said.
"I then turned the bunny around to see it said 'dairy fine' on the front, but it was very hard to see."
In a matter of minutes, Drummond had an epipen administered and an ambulance took her to hospital.
She spent the night in ICU as doctors gave her multiple doses of adrenaline to help reduce swelling in her throat.
"I'm still very unwell but I'm past my anaphylactic reaction and I'm very lucky that I did get through it," she said.
"It's one of my worst reactions."
CEO of Allergy and Anaphylaxis Australia, Maria Said, told 7NEWS.com.au the "dairy fine" label should be scrapped.
"We're not just talking about a rash here, we're talking about life or death," she said.
"If they do keep the 'dairy fine' brand, it's got to be in a clear, bold font legible on foil and cellophane.
"Thankfully she survived, but we've had many, many people make the same complaint.
"They (Aldi) don't want to wait for a fatality to finally make a change."
Said commended Aldi on expanding its range of chocolate for people with allergies.
But she says addressing the "dairy fine" label should be a priority.
Drummond says she hasn't yet brought the episode to Aldi's attention but is intending to.
"I’ll definitely be taking it further. Their packaging is very misleading and not clear."
A spokeswoman for the supermarket giant said it could not comment on the issue as it had not been reported to them.
However, if a health issue was brought to its attention, she said it would file a report to the food safety authority for a review.