It is normal to have little white dots on gums after dental implant a month ago? (Photo)

Go back to the surgeon to make sure you don't have an infection. Although not normal, the spots don't appear to be a serious issue, but better to be safe.

Hello! I think you have a possible infection from how I see from the photo. Possible periimplantitis. Go back to your doctor and check for it and also you can do an X-ray to check for bone retraction or infection. 
Sanatate!

It’s hard to tell from your photo, but if a bone graft was done at the same time as the implant placement, then it’s possible you’re seeing some of the graft material itself. 
It’s also possible that an infection may have started, so your best course of action would be to have your dentist take a look.
I hope you found this information to be helpful,
Dr. Champagne

It is likely occurring due to improper brushing / hygiene.  With braces, you have to be much more diligent with brushing your teeth and gums.  Next time you see the dentist, talk to them about it.