Hello Hiro! Great job with the diary post, it's totally understandable and very clear! :D 

There are a few small errors, mostly with synonyms and prepositions, but I was very picky with them. If you fix those, you'll sound like a native in no time! c:

I have been looking after a 6 years old girl as a babysitter in Australia since July. (you don't have to say "as a babysitter" since it's implied by "looking after") Although I have younger siblings back in Japan, it is my first experience to look after kids. (first experience looking after kids) The purpose that I chose this job was improving my English skills. (The reason why... was to improve my English skills) The family who I work for is Australian (I work for, no need for who c;) and luckily the girl has had some asian babysitters before me, so she can understand me very well even though I have thick accent in my English. (have A thick accent in English) Basically I like kids but the girl is especially adorable for me. (Basically sounds a little odd here, maybe "in general" would work better) She is kind of wild, does not stop chatting and does not run out of energy. On the other hand she is easily scared. She can not go into a dark room by herself. (cannot is usually reserved for emphasis, most people just use can't c;)

In these days she keeps watching Harry Potter movies. (Just "these days") Literally everyday, sometimes from early mornings. (every day) She almost remember every single words the characters say and what happen next on the movie. (she almost remembers would mean that she can't quite remember the words. I believe "she remembers almost" would work better, meaning she remembers most of the words) It reminds me of my younger brother. (That instead of it, or else it sounds like you're referring to the girl as "it" :D) When he was a kid he kept watching the same movie everyday and made the other family members got sick of it. (made the other family members got sick --> made other family members get sick)

I am staying with her this whole weekends but I am going to leave this position soon for some reasons. (whole weekend, since it's only one weekend you're referring to c; "for some reasons" sounds like you don't know the reason why you're leaving. If you do know the reason but don't want to disclose it, it's better to just say "I have to leave this position" or just skip "for some reasons" as a whole) I definitely will miss her. I wish we can meet each other sometimes ninth future :) (sometime in the future* c; - she sounds delightful, and I hope you do get to meet in the future c:)

Hope this helps and best of luck! 

Diary 9/9/2017

Hi! Could you please someone correct my english? I only know and use easy words but I would like to get more vocabulary or idioms to make my english sounds more natural so if you think other words are more suitable in these sentences please don't hesitate and correct them strictly! Thanks in advance :)

I have been looking after a 6 years old girl as a babysitter in Australia since July. Although I have younger siblings back in Japan, it this is my first experience to look looking after kids. The purpose reason that I chose this job was improving to improve my English skills. The family who I work for is are Australian, and luckily the girl has had some asian Asian babysitters before me, so she can understand me very well even though I have a thick accent in my English. Basically I like kids but the girl is especially adorable for me. She is kind of wild, does not stop chatting and does not run out of energy. On the other hand she is easily scared. She can not cannot go into a dark room by herself.

In these These days she keeps watching Harry Potter movies. Literally everyday, sometimes from the early mornings. She almost remembers every single words the characters say and what happens next on in the movie. It reminds me of my younger brother. When he was a kid he kept watching the same movie everyday and made the other family members got get sick of it.

I am staying with her this whole weekends but I am going to leave this position soon for some several reasons. I definitely will miss her. I wish hope we can meet each other sometimes ninth in the future :)

Your English is fantastic - great job! I changed some of the word choices (in green) to sound a little more natural to a native speaker.