*My sweet dog*

Today I introduce my sweet dog, her name is Honey.
She always beside me in my house.
I feel healed just when she is there.
She is 4 years old and a really clever dog.
Every morning, she comes in my room to wake up me so
I don't be oversleep. I'm grateful for her.
Sometimes I take along her to her favorite park.
I'm glad to see her happy face.

*My sweet dog*

Today, I introduce my sweet dog, her name is honey.
She is always beside me in my house.
I can become healed just by her being there. she is there.
She is 4 years old and a really clever dog.
Everymorning she everyday comes into my room to and wakes up me me up so
I don't be overslept oversleep. I'm grateful for her.
Instead Sometimes I take along her to her favorite park.
I'm glad to see her happy face.

英語は難しい言語ですが、泉美さんは英語を話すのが得意です（違う漢字を使ったらごめんなざい）
アメリカに生まれましたけど、まだ英語は難しいと思います。　 

*My Sweet Dog*

Today I introduce my sweet dog, her name is Honey.
She is always beside me in my house.
I have a good feeling (can healed) just to know she is there.
She is 4 years old and a really clever dog.
Every (At) morning she comes into (everyday come in) my room to wake up me so
I don't oversleep. (be overslept.) I'm grateful to her.
As a reward, (Instead) I sometimes (I) take her along (her) to her favourite/favorite park.
I'm glad to see her happy face.

Yes, very cute dog, Izumi. With a title, we always show this with initial capitals to stress its importance. Apart from that, I have suggested a few phrases which you can use to improve your writing. Well done. Nice article. 

*My sweet dog*

Today I will introduce my sweet dog, her name is Honey.
She always beside me in my house.
I can healed feel better just because she is there.
She is 4 years old and a really clever dog.
Every day in the morning she  comes to my room to wake up me so
I don't oversleep. I'm grateful to her.
Sometimes I take along her to her favorite park.
I'm glad to see her happy face.

Hello Izumi, she is such a cute little dog isn't she.

Just a few small mistakes in your text but I understood everything

1. In English, proper names (like Bob and Izumi) always begin with a capital letter, even for animals names.

2. Healed is ok but it is more natural to say 'I feel better'

3. With adjectives (describing words) you can say 'She is really clever' but if there is a noun (thing) after the adjectives then you must use 'a' if it is one thing. "She is a really clever dog"

Hope this helps

*My sweet dog*

Today I introduce my sweet dog, her name is honey.
She is always beside me when I'm in my house.
I get healed just when she is there.
She is 4 years old and is a really clever dog.
In the morning she comes in my room to wake up me so
I don't be oversleep.I'm grateful to her.
Instead sometimes I take her along to her favorite park.
I'm glad to see her happy face.