Is it okay to consider publishing in my first year of PhD? I'm PhD candidate in Applied linguistics, it's been almost 3 months since I've started but I'm seriously allowing for writing and publishing journal articles.

I have asked my supervisor about that, she said that I should devote my time to my thesis and wait until the second year and that writing other forms of papers generally interfere with the thesis. 

However, I think I have enough time to simultaneously work on my thesis and also articles, also I have to indicate that the ideas that I'm willing to formulate in articles are not related my PhD focus.

What should I do? Should I wait until next year or just start working on articles and submit them as single author?
Whatever you do, you will want to cultivate a good working relationship with your supervisor, so I'd advise against doing something she dissuaded you from just because strangers on the internet told you to. Talk it out with her.

That said, not a single PhD student I've known wrote/writes a relevant portion of their thesis in their first year, and the advice I have constantly been getting from faculty is that early in the PhD is the time to think about publishing other things. There will most likely be a time when your thesis takes all your attention, and by then it's certainly too late to worry about publishing elsewhere.