IVF (in-vitro fertilisation) requires many injections, including follicle-stimulating hormones to increase the number of eggs growing in the ovaries.
Elonva is a sustained follicle stimulant given in a single injection. It can replace what is usually a seven-day course of one injection a day.
It was registered in New Zealand in March last year, but its maker, Merck Sharp & Dohme, is only now starting to promote its use here.
Ms Gray, 37, said she and her husband, Tim Jones, got tested before they started trying to have a baby, "because of my age".
"Rather than spend years trying first [we decided] let's get tested.
"It was about 12 months previous to starting IVF that we found out IVF was what we would have to do."
They paid privately for IVF treatment. The first embryo implantation didn't work, so they waited a month and had one of their frozen embryos - created from the initial treatment and frozen - thawed and implanted.
This time Mrs Gray became pregnant, resulting in the birth of Daisy, who is now 14 months old.
Dr Birdsall said there was caution about giving the new drug to women with polycystic ovary disease because of the risk of ovarian hyperstimulation syndrome, a potentially life-threatening complication of IVF hormone treatment.
However, techniques were emerging that could mitigate the risk.
"There are some innovations we can do to take away that risk," Dr Birdsall said.
"People hate the injections as part of IVF and this is a real step forward in terms of reducing the amount of burden associated with the treatment."