。
How about consulting a doctor and having them prescribe a sedative for you?
Literal
Doctor [to-に] consult-and sedative [object-を] prescribe-get-done [nominalizer-の][topic-は] how [would-it-be-でしょうか].
A polite suggestion. The frame ~のはどうでしょうか ('how about X?' 'how would it be to X?') is the standard polite way to suggest a course of action. Inside, 処方してもらう uses the ~てもらう pattern — 'have someone do X for you,' specifically framing the action as a favor or service received from the doctor. The whole verb phrase 医者に相談して鎮静剤を処方してもらう ('consult a doctor and have them prescribe a sedative') is then nominalized by の and made the topic. Note that 医者に (to a doctor) uses the dative に, both for 相談する (consult) and for ~てもらう (have done by).