She is proud that her son became a doctor.

Literal

She [topic-は] son [subject-が] doctor [to-に] became fact [object-を] pride [adverbial-に] is-thinking.

Variant of the Xを誇りにする pattern — here Xを誇りに思う, with 思う ('think, feel') instead of する ('make X into Y'). 誇りに思う leans more 'feel pride' (subjective experience), while 誇りにする leans 'take pride in' (deliberately treat as a source of pride). Both are in everyday use; the latter is slightly more performative. The fact-clause ~ことを uses the こと nominalizer to make 'the fact that her son became a doctor' the focus of the pride.