Flu virus. Will baby be ok? (Vaccinated)

I received the flu vaccine while pregnant with my little one. My husband forgot to get vaccinated, and is currently showing flu like symptoms. We’re doing our best to keep him away from our baby (7 weeks old). Since we were vaccinated, is my baby safe from getting the flu?

Side note: we have a doctors visit scheduled to see the pediatrician in a couple days in case baby starts to show symptoms. The only thing he has now is a stuffy nose. But that’s not uncommon for him.