Mrs Lake told Fairfax Media the family took Penelope to an after-hours clinic in Newton, and was then taken to Wellington Hospital, where she died that night.
She did not know a vaccine was available.
"We did all the right things," Mrs Lake said. "It just works so fast."
There have been 11 cases of meningococcal disease in the Wellington region this year, the latest a baby who was hospitalised on Friday with the disease.
Deputy director of health Darren Hunt told Newstalk ZB vaccinations are affective at stopping the spread of the disease.
"The vaccines for meningitis are pretty good in outbreaks," he said.
However unlike vaccinations, the one used to combat meningitis does not last forever, rather only lasts three or four years, Mr Hunt said.
While in Northland there have been several cases of the type C strain of the disease, in Wellington all different strains have struck victims.
The B strain, which is the most common, does not yet have a vaccine, Mr Hunt said.
"Meningococcal disease is a pretty devastating illness so it is always a concern when hear of cases."
Symptoms can include stiff neck, painful limbs, bad headache, vomiting, fever, drowsiness, a baby refusing feeds, and a rash.
Urgent medical care should be sought for suspected meningococcal disease, which is readily treated with antibiotics if detected early.
- Herald Online staff
