Can you still have godparents even though your getting baptised at 16?

I cannot see a reason why you cannot.

The modern view of a godparent tends to be an individual chosen by the parents to take an interest in the child's upbringing (esp. in case of the parent's death). You always have a mother and a father. You always have godparents.

In my own family it was quite nice to be offered the ability to be a Godparent. I offer you my own belief on the matter.

Godparent is a role not only in the Catholic denomination but it also exist in other christian denominations as well.