正确。
enjoy oneself doing sth.玩得开心,过得愉快。
或者说enjoy oneself in doing sth.意思一样,但in可以省略。
拓展阅读：
英语固定用法：enjoy doing sth.
enjoy享受；欣赏；享有；喜爱；喜欢；享受??的乐趣；享受?乐趣
enjoy oneself 过得快乐，过得快活
enjoy life 享受生活；享受人生
enjoy yourself 过得愉快；请自便
enjoy your life 享受生活
enjoy doing 乐于做?，喜欢做?
例句：
She thought that husband and wife should enjoy a little of that isolation to which marriage had indissolubly doomed them.
她认为这对夫妻应该享受一下婚姻永久赋予他们的与世隔绝小日子。
Now if we have indigestion,it's very difficult to enjoy food.
如果我们消化不良，那很难享受美食。
One question is: how much privacy should public figures enjoy?
一个问题是：公众人物究竟享有多少隐私？
Most people enjoy receiving letters, but few seem to be very fond of writing them.
多数人喜欢收到信件，但似乎没有人喜欢写信。
Oh, I can enjoy reading on this balcony in a fine day like this.
噢，我可以在像今天这样的好天气在阳台上看书了。
I did not enjoy it. A young man and a young woman were sitting behind me.
可是我却无法欣赏。我的后面坐着一对青年男女。
It is not how much you have but how much you enjoy that makes happiness.
使你快乐的不是你有多少，而是你享受多少。
What's with you? Uh, nothing, nothing's with him. Enjoy your coffee.
你怎么回事？！啊他什么事都没有，好好喝你的咖啡。