Bubbalicious, designed and developed by digital marketing agency Neoco, offers support and safe sleep tips for both mums and young dads.
Users can chat, win prizes, upload photos and take part in a four-level baby-care challenge.
If successful, they are awarded the title of "Top Dad" or "Big Sister", which allows them to give advice to other parents on the site.
Figures released last month from the Office of National Statistics reveal that mothers under the age of 20 are over four times more likely to have a baby die as a cot death than older mothers.
Joyce Epstein, FSID's director, said: "Sadly, the latest research shows that teenage mums have the highest rate of cot death, but we think that many are missing out on safe sleep advice.
"We developed bubbalicious after consulting with young parents across the country, and we really hope that the support available on the site will help improve the life chances of the UK's most vulnerable babies."
The FSID works to prevent sudden deaths and promote infant health. It funds research, supports bereaved families, promotes baby care advice, and works to improve investigations when a baby dies.