Whilst no 'formal' qualification is 'required' to become a singing teacher or vocal coach, it is in both your interest and that of your pupils to gain as much knowledge as possible. A qualification also gives your future potential clients peace of mind in your capabilities.
I wouldn't say you were too old to go to uni .. there are plenty of people of your age and older who do so, however, it isn't the only option available so maybe one of the others will appeal more ;-)
1. Individual training - Private tuition from a fully qualified teacher who provides teaching to exam level in voice.
2. Colleges - Provide full and part time courses in voice, theory and the teaching of voice to degree level (i.e., Institute of Contemporary Music )
3. Music organisations provide courses/workshops like the The Voices Foundation or can advise on courses available like the Association of Teachers of Singing, Musicians Union, National Association of Music Educators and The Arts Council of Great Britain
4. Companies/Teachers who run courses/training in specific methodology founded by individual teachers like Estelle Liebling or Speech Level Singing (Seth Riggs).
There are also several good books that provide a wealth of research material for both teachers and students on the voice. Some of which are listed at our parent site Vocalist.org.uk in the Singing Instruction Books sections. Whilst these are no substitute for a qualification, there are some listed by respected authors whose works are often used as a reference source by teachers and course trainers alike (i.e., Richard Miller, Clifton Ware, Oren L. Brown etc.)
Hope this helps