My father is a doctor, and I intend to become one too.
Literal
Father [topic-は] doctor is-and, I [also-も] doctor [into-に] let's-become [quotative-と] think.
~であり is the copula's continuative form, linking clauses in a written/formal register. ~になろうと思う combines the volitional form of なる with と思う to express a considered intention — 'I intend to become a doctor too.'