Applying for a new job if i'm not happy with my old one?

I'm applying to burger king and i'm writing a message to the employer as to why i think i would be a good fit and have I have the qualities listed because my job right now i'm working at a food place. Do i say i'm looking for a new job and I have the qualities listed because I have experience? Can they call my boss? Cause idk what she would say. I think i'm a hard worker but i dont know if she would say good things about me or bad and i wouldnt wanna ruin a chance at a future job since i'm not happy at my current one. Also updating my resume so would I put my current job on there?? 😐