Yup. Submit your application on the company's website and keep on updating it; they'll call you if/when they need you.
However, with your type of experience, it would probably be the A320 for you, and that is the only significantly growing fleet for which they plan to employ more pilots right now. In a way, you are therefore better off than some Captains looking for a 330- or 777-job.
How serious is etihad airways about 500 hours on the aircraft type they fly
They are very serious about it.
Depending on your personal circumstances of course, my advice to you would be to look for a A320-job first, and gain some hours for a year or so - which you'll have to wait anyway. Once Etihad begins to recruit larger numbers of pilots again, you'll then be ready for it.
I know nothing much about other companies, but another option for you might be to try places like Flydubai or Air Arabia. They operate 737's, and for that you are more qualified with your rating.