As a newbie to ADX, and just finding myself fresh out of training, I can add that finding a job as a newly qualified dispatcher depends on how motivated you are. I have absolutely NO AVIATION experience either except for a short stint with Northwest Airlines.
My recent experience with finding a job as a newbie is as follows:
Before I started my training, keeping in mind that not only was I going to the class but also I was determined to get my license, I started applying for jobs. The theory was that it would take HR a bit to sift through every submitted app. That being said, I took advantage of this delay to beat any application deadline especially for the airlines that don't post job openings often (sometimes ADX jobs are posted for only a few hours!). I also took advantage of this lag, knowing that if an airline got back to me, I likely would have a little bit of time in training under my belt.
Next, I continued to apply for jobs while I was in training. This is tough to do considering there is a lot of work to do in training, but it can be done. After all, the goal for going to dispatch training is to land a job, right?
Finally, and I am not kidding when I say this, I was interviewed and hired for a 121 carrier inside of about two weeks into my training. To echo what pljenkins said, and correct me if I am wrong but I believe he is involved in hiring for a major airline, my airline was eager to hire me because like most middle aged professionals going through a career change, I had a ton of experience outside of aviation that would be beneficial to any airline. Needless to say, my new airline new I was brand new to the profession and when I interviewed, they weren't interested in what I had learned from my training at that point - they really wanted to know how I could apply my previous experience to the dispatch role.
If you find yourself not having a lot of professional experience, you are going to have to make the necessary connections from your previous roles to help HR or those who are interviewing you with how that small amount of experience can assist with dispatching. Though those roles will be different from a dispatcher, there are always basic-core elements that will transcend into dispatching such as multi-tasking, working in a high stress fast paced environment, professionalism such as having good performance evaluations, no disciplinary actions, etc.
On another note, as I was going through my training, several of my classmates did not apply for work. Instead, they wanted to wait until they were done with training before they started in on the hard core job search. I think that this is a mistake. Even though there is a lot of work to be done in training, many of them thought searching for a job was too time consuming and took away from studying. Depending on the person, this may very well be true but it only hurts you in the end for not taking advantage of applying for open jobs. We had 18 students that started the class. I would estimate that only about 1/3 of the class applied to jobs during training. The other 1/3 was already employed for an airline. This left about six students who were not taking advantage of applying for jobs. I am convinced to a point that even those that were applying for jobs, were only doing it on a limited basis. That being said, and I am sorry to put it this way, but your classmates are your competition in the job market so take advantage of applying while you are in class when your colleagues aren't on the hunt.
Additionally, where I went to training, the staff helped immensely in crafting and perfecting resumes that are acceptable/preferred for the airline industry. Also, the school routinely circulates a list of open jobs to all students and alumni. Some airlines even contacted my school looking to interview students for a position. The training center was pretty proactive submitting the entire classes resumes to other airlines that had job openings. Even though a lot of the jobs posted were looking for one year of experience at a minimum, don't let this dissuade you. I was actually interviewed for a dispatch supervisory role my first week of training and I had never seen the inside of an operations center. This just goes to show you that regardless of what the job specs are, apply - you never know. If you don't apply, the answer will ALWAYS be NO!
As you can see, there is interest in hiring new dispatchers. You just have to work for it to make it happen. Case in point, there is a former student at my training facility that has not found a job in about a year after getting their license. This person had too high expectations with each of the jobs they interviewed for and has yet to accept employment anywhere. They have relied solely on the school to help them land a job and have not done the ground work on their own to find employment.
On a final note, I have found that this job is generally in demand. Though the major airlines may not necessarily be hiring, that should not be an indicator of the job market. A ton of work is available in so many different areas that require you to have your airman's certificate, not just dispatching. I have also found that the dispatch community is rather small when all things are considered for other professions. That being said, when a lot of work is available and you have a fairly small pool of qualified candidates applying for jobs, taking a new guy fresh out of training makes sense. Also, you have your license. This means, even though you may not have a lot of experience, you are just as qualified as me and all the other dispatchers on this forum to do the job. How well you do it is another issue, but still you are just as qualified as the rest of us. From one newbie to another, drink up pal and enjoy the ride and APPLY!
Present gig I'm back in the trenches, and loving it!