She is thinking of marrying her daughter to a doctor.
Literal
She [topic-は] daughter [object-を] doctor [with-と] marry [causative-させよう] [quotative-と] is-thinking.
結婚させようと思っている — the causative 結婚させよう ('let/make marry') with the volitional and と思っている ('is thinking of') expresses her plan to arrange the marriage. Causative here implies parental influence over the daughter's marriage.