用法是對的
suggest doing sth建議做某事（動名詞作賓語）
suggest sb's doing sth（動名詞作賓語帶有自己的邏輯主語sb's：所有格+動名詞，叫動名詞的復合結構)
suggest sb doing sth（動名詞的復合結構作賓語時，可以用代詞賓格或名詞普通格代替）
例子：
I suggested his leaving soon.
=I suggested him leaving soon.
I suggested the boy's leaving soon.
=I suggested the boy leaving soon.