No, it is actually good to have some baby teeth in the mouth when starting braces.
Baby teeth are bigger teeth compared to their adult tooth underneath and this extra space can be used to alleviate dental crowding. Also, the severity of some orthodontic problems, like upper canine teeth going off course, can be reduced by early removal of baby canine teeth.
Your dentist should be able to pick up on this and refer you to an orthodontist. Or, you can go directly to an orthodontist for them to check.
To find an orthodontist near you, click here.