。
She's happy to be carrying his child.
Literal
She [topic-は] his [genitive-の] child [object-を] pregnant-and happy is.
妊娠する ('to be pregnant, become pregnant') takes the carried child with を — 子を妊娠する, somewhat unusual since most pregnancy verbs in English don't directly take an object. The te-form 妊娠して links the cause/state ('being pregnant') to the result (幸せです, 'is happy'). 幸せ ('happy') is a na-adjective; here just predicate with です. The polite ending suggests this is reported or shared speech.