Most companies in the US like you to work for at least one year before moving on. Some even have direct wording that HR dictates to management about this. I have managed at two such companies.
My advice is talk to fellow employees (not managers) and just ask them if there is time span needed before moving on to another position after starting with the company. This is usually common knowledge at most places and given you have been there 6 months you should know enough people to get a solid answer.
If this fails you could bring it up to your manager. But I would bring it up in more of a hypothetical way not that you are looking to leave right now. Saying something like, "I am looking at mapping out a progression plan. Are there any company guidelines or rules about when we can start applying for different positions? I am wondering if I saw something in the future at what point is it OK to have a talk about advancement."
Note that there is a risk to even saying something like this. If the manager knows that you are a flight risk after 6 months they are less apt to give you a larger yearly raise, bonus, or good marks. This all depends though on your exact situation. If you are somewhat disgruntled (because you don't like your job) and an average employee, I would not be happy as a manager. Good chance we spent 3-5 months training you and then as soon as you didn't want the job you want out.
As an unhappy manager I could talk about you with other managers. These other hiring managers would know that you might be apt to not like your new job in their group too and want out in 6 months. Some might not even interview you and in one company I worked in I saw that several lower level employees got stuck in their positions until they either waited out the bad karma or left.
Now if you are a really good employee and doing a great job then this is a different conversation. Your manager might tell you that you basically need to wait a year (maybe they say you don't have to). Also your manager may be willing to alter your job or to find a promotion under them so that they can keep a good employee.
So really this conversation is about you. I have had many employees come in and have talks with me about this and most (not all) were below average. And it was usually at 6-8 months. I would almost snicker... like you don't even know this job and you want this other job? If you aren't in this category great for you (and things will probably work out either way) but be cautious.