My daughter has a very strong regional accent. My husband and I don't. I know it comes from nursery as all the staff have this accent. And the slang words.....oh I hate the slang words. She talks about "mah" instead of "my" etc, oh and once told me "I'm pure soakin so ah am" I correct the slang and pronunciation, and she is slowly learning. It bothers me because she spends more time with us than at nursery, but theirs is a stronger accent. Neither my husband or I have strong accents. She did go through having an english accent and even copies some american accents. None of it lasted long.
I'm sure she'll grow out of it, I had an English accent at her age, despite my parents having strong scottish accents. Then I moved to scotland and found that children hit you if you speak funny. My accent changes depending on where I'm travelling to. As I go south I get more english and as I go north I get more of the Scottish Accent I grew up with. I never notice it, but my husband does!
I think suggesting speech therapy is a bit drastic. My SIL is a pediatric speech therapist. Her take on it was, children will pick up on their strongest influence. Making too big a thing about it may well stop them from exploring language and thats not something you want.