However, the reason for her hair is heartbreaking.
The youngster was not only born with Beckwith Wiedemann syndrome - which means she will grow considerably larger than her peers - she also has hyperinsulinism, which is thought to be the reason for her hair.
Hyperinsulinism, which is described as being the opposite of diabetes, can cause brain damage, blindness and death, and the drugs to control her insulin levels is what increased her hair growth.
Little Penelope has had a rough start to life, being put on a life support machine called EMCO after she developed meconium aspiration syndrome, which is when a baby inhales poo before or during birth. She was then diagnosed with hyperinsulinism before doctors confirmed she has Beckwith Wiedemann syndrome.
Talking to The Mirror about her daughter’s early days, her mum, Gianna Pickup, said: “When I was first able to go and see her, I struggled to comprehend the severity of the situation.”
"These were all words to me, all I knew was that my baby was ‘dangerously ill’ in the doctor’s own words."
Describing the rarity of her child’s condition, Penelope’s mum said: “It is such a small cross section of babies who have both hyperinsulinism and Beckwith Wiedemann. It's about one in 150,000 in fact."
However, despite strangers constantly thinking her little girl is older than she is, Gianna, who is expecting her second child, says she now laughs it off.
