Welcome to allnurses!
Most agencies require a minimum of one year clinical experience before they will sign you up. However, many
hospitals that use travelers require two, three, or more years of experience, so, even if you are signed up with an agency, the agency may have a hard time finding an assignment for you without significant experience.
Hospitals pay a
lot of money for travelers. For that amount of $$, they are expecting (and
deserve 
) to get a seasoned "pro" who is ready to walk in and do the job, to "hit the floor running." Travelers rarely get more than a shift or two of orientation (if that much), and are expected to function independently with minimum supervision/assistance. Also, the staff nurses are well aware that you (as the traveler) are getting paid quite a big more money than them to do the exact same job, so they're often not inclined to help bail you out if you get into trouble.
I encourage you to take a look at some of the recent threads on this forum about bad experiences some of our posters have had on assignments -- it's not that uncommon for hospitals to be using travelers because morale and working conditions are so bad at the facility that they can't get the local nurses, who know what things are like there, to work for them.
The travel nursing agencies are in business to
make money; you cannot depend on them to look out for your best interests. If you crash and burn, they have plenty of other nurses, but
you only have
you. It's important to not only have the necessary clinical experience, but
also to be experienced and savvy enough as a nurse,
in general, to be able to look out for your own interests and protect your license.
This is just one person's opinion, but I doubt anyone here will tell you anything much different. Travel nursing can be a terrific opportunity and lifestyle for the people who like it, but it's definitely not for newbies. You will find that it takes you a year or so, as a new grad, to start to feel confident and reasonably competent in a job where you work in the same environment, with the same people, day in and day out -- how long will it take you to feel like you could walk into an unfamiliar environment, with possibly v. poor working conditions, staff morale, etc., and be able to function competently and independently? When you get to
that point, you'll be ready to think about traveling.
Congratulations on your graduation, and best wishes for your new career --