Can I apply for this job (details included)?

Ok, someone at my office quit and they are currently hiring a replacement. I think I would do the job just find. I'm qualified and have worked in that office for 1 year so far. In the past, they always ask the people who work in the same dept. if they would like the opportunity to advance and take the available position, but this time around they didnt ask me and I dont know why. I'm hurt. But I'd like to apply for this position since nobody asked me. So my Question is, am I allowed to send my resume the way everyone else applying for this job is doing? Or is that like a big no no?
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Don't send your resume as you aren't an outsider. You really need them to hire you as an internal application, right?

Take a deep breath and pull yourself together. Meet your superior officer and ask him/her to make a written recommendation for you to get the post.

Make 3 hard copies for the internal application resume and send 1 to your Human Resource Manager, 1 to your superior officer and another 1 for you to keep.

What are you waiting for? Go, do it now!