I will answer your question in 2 parts:
1) How to tell if the practitioner is a doctor
2) How to tell if the doctor is trained to perform filler injections.
With regards to the first part, you can search the Singapore Medical Council register of registered doctors online (https://prs.moh.gov.sg/prs/internet/profSearch/main.action?hpe=SMC).
Alternatively, you can ask your doctor to show his/her Singapore Medical Council registration card or certificate.
All doctors practising in Singapore have to be registered with the Singapore Medical Council, regardless of the university that they graduated from.
How to tell whether your doctor is trained is trickier. You can ask to see the doctor's Certificate of Competence (CoC) for filler injections. It is mandatory for doctors to obtain this CoC in order to practise aesthetic treatments.
Unfortunately, there is no register available to search for the public to search for this. You can also have an idea how 'trained' the doctor is by asking about the experience and patient pictures that he/she has.