It was announced this week that Moyer and his co-star wife Anna Paquin are expecting their first child.
Gavankar, who plays Luna Garza on the HBO drama, spoke to Us Weekly about Moyer's two chidren from previous relationships
She said: "Stephen... is such a proud father, and so light-hearted and shiny."
Revealing that the elder of Moyer's two children, Billy, had recently spent time on the show's set, Gavankar labelled the 12-year-old "such a sweetheart".
> Stephen Moyer 'wasn't looking for love on True Blood'
> Stephen Moyer: 'Anna Paquin relationship is a cliche'
Watch the first teaser for True Blood's fifth season below: