How to transfer departments at work?

I recently started working for a large company (ISP) doing SysAdmin work. I was looking for more of a network admin position but I took the job. A coworker I knew from another job recently got hired as well but in a slightly different department (technically it’s the same department but he is under a different manager doing different work). Our teams sometimes work together. His job consists of what I want to do, his team frequently works from home, his days are shorter, and we get the same pay as the company sets a standard rate for all system\network engineers.

I would like to transfer to his department but I have only been at the company a week. I am not sure if it would be more respectful to bring it up now so that they don’t waste resources training me or wait about a year.

How would you handle this?