She said let's call a doctor right away.

Literal

She [topic-は] right-away doctor [object-を] let's-call [quotative-と] said.

呼ぼう is the volitional form of 呼ぶ ('to call / summon'), proposing an action. Inside a quotation marked by と, the volitional becomes a reported suggestion or intention — 'she said "let's call"' or 'she said she would call'. The structure VOL + と + 言う is a standard reported-suggestion frame. The whole sentence reads as a snapshot from an emergency moment: someone is hurt or unwell, and her response is to suggest summoning medical help.