To answer some points aimed at my pp, no, the world has not got more dangerous since we were children and did babysit at age 12/13, but societies attitude and the attitude of the legal system and child protection agencies HAVE changed.
Leaving a baby with a 12 year old, or any other child under the age of 16 (and even a "child" between the age of 16 and 18), could leave you, as the adult, legally responsible for any harm that comes to the baby. Check out the advice on NCPCC and similar websites.
Accidents do happen. Children do things they are not supposed to do. Imagine the 12 year old (or the 9 year old) decides to cook, and manages to start a fire, or the baby wakes and the older child feeds it something, and it chokes, or as it has a dirty nappy, and the older child decides to bath the baby........ many unexpected things may happen and the older child/children may not act in the way they have been told, or in the way you would expect your mature under 16 year old child to react. They may panic, they may not act quickly enough.
If your baby/young child were to land up in hospital because of similar scenarios to those I outlined above, SS would be very interested in looking into the fact no adult was present (my DH has a child protection role as part of his job, and 2 cousins are SW).
I have an 18 and a 17yo DS, a 14yo and a baby, I would NEVER leave the baby in the care of the 14yo, and have only briefly with the 17/18yo.