Her mum Kellie Burville, 27, from South London developed a rare condition in pregnancy that caused her body to attack her unborn baby. Doctors told her that Logan would be so severely brain damaged that she wouldn't survive and she was given the option to have a termination. Kellie refused and bravely continued with her pregnancy.
At 36 weeks pregnant, a consultant told Kellie and her partner Callum Campbell, 23, a labourer, that their baby had suffered a brain bleed and she would be severely brain damaged.
They were told she was not expected to survive and the couple were offered a range of options, including a termination. A scan showed Logan's head was twice the normal size because of the amount of fluid on her brain and a natural birth would be impossible.
"Our whole world fell apart in that moment," says Kellie. "I looked at Callum and burst into tears. I'd just had my baby shower a couple of days before. We already knew we were having a girl and had bought everything for her. We'd been so excited.
"The doctor explained that if she did survive, she wouldn't be able to walk or talk. She wouldn't be able to feed and wouldn't know who we were.
A Caesarean section was scheduled the week before Kellie's due date and Logan was born weighing 5lb, 5oz.
"They had already told us they wouldn't do anything for her or give her any treatment after she was born," says Kellie.
They weren't expecting her to live. Callum and I tried not to think about it but we picked some songs we wanted playing at her funeral. We were given a bereavement blanket to wrap her in and a Moses basket.
Tests revealed Logan had a platelet count of just five - dangerously low. A newborn baby should have a level between 150 and 450, so Logan was given a blood transfusion to help boost her platelet levels.
"It was amazing to hear her cry. Our little girl was alive," says Kellie. "Her head was normal size and she started feeding straight away. A midwife asked if we wanted to see a chaplain to get her baptised. My tummy had already been blessed before the birth. It was such a happy time and for her to come and say that burst our bubble."
An MRI scan the next day showed fluid had built up in the brain, pushing it against the skull and causing a brain bleed.
Doctors were still baffled by what was behind it and initially put it down to an infection during pregnancy. But at four days old, Logan was diagnosed with the potentially fatal Neonatal Alloimmune Thrombocytopenia (or NAIT), where the mother's body treats her unborn baby as a harmful invader.
The condition causes the mother to make antibodies that attack the baby's platelets. This can cause babies to bleed into their brain, stomach or spinal cord during pregnancy or shortly after birth. Babies can be at serious risk of brain damage or even death.
It is so rare, the condition was only discovered after Kellie's sister typed Logan's symptoms into an online search engine and came across a charity called Nait Babies.
She passed the information onto doctors and a simple blood test confirmed the diagnosis. Doctors were happy with Logan's platelet count and amazingly, she was allowed home the same day. Four months on, Logan has confounded medical opinion and her parents believe she will live a normal life.
"She's doing everything you would expect of a healthy baby. She's hitting all her milestones," says Kellie. "Her consultant said babies are very resilient. They can use other parts of their brain. She's my little miracle."
"I was scared but I didn't want to express how I felt because I had to be there for Kellie," says Callum.
I had to stay strong but inside I didn't know what would happen. Logan is doing really well. It's amazing to see her doing all the things the doctors said she wouldn't be able to do.
A spokesman for Chelsea and Westminster Hospital said: "We fully supported Kellie and her partner in their choice to continue with the pregnancy and we delivered their baby by Caesarean section and then provided treatment after Logan was born on our Neonatal Intensive Care Unit. We are delighted that Kellie and Logan are doing well and we wish them well for the future."
For more information, visit Naitbabies.org.