Is it important to have good Arabic to do well in your career in Dubai?

I guess it's a must to simply survive there, but to have a great career you need much more than that, especially in a highly competitive place like Dubai !

yes you can be acareer job by learning Arabic language 

I don't think it's going to boost your career neither send it backward.
Dubai is a very open country where the population is most of it composed by foreigners.
For me knowing more than2 languages is ALWAYS a plus and needed, to show you can adapt quicker than others...but that doesn't especially mean that you're smarter.

yes , beause in the dubai most of people arabic spoken and govourment language also arabic so good arabic help to well career in dubai.