Take the plunge
Is three years in the job as a teacher enough to become a head of department?
In any letter of application you are trying to answer two questions: can I do the job? And why do I want it? Start by looking at the person and job specifications. Then try to match up your experience with what is required.
The better the fit, the more chance you stand of being interviewed and even being offered the post. However, some jobs attract far more applications than others and this will affect who is selected for interview. As to whether three years is sufficient experience: ask yourself whether others will have more and better experience and why you want the job now? Have you enjoyed your period as an acting head, and if so, why? Some schools may regard three years are insufficient and others as showing keenness. You will have to address the issue either in the application or at interview, so think your answer through.