This genre was one of my favourites as a young reader. You've made a good start with this opening sentence.
Here as a few things to consider:
- Keep in mind the vocabulary you are using is appropriate for your audience. If this piece is aimed at the 7-8 year old audience, the words "constituted" and "accustomed" may be a bit of a stretch. Keep this in mind as you continue with the story.
- Personalise the characters- "...without the investigator's kit..." could be turned into my investigator's kit. Also, the phrase "Mother cleaned my room again" seems distant.
- I'd love to hear about the latest article Julia had her eye on in the detective magazine... perhaps it could be relevant to her new case?
-I'm not sure if the paragraph that introduces her mother is necessary at this point. You could turn it into dialogue between the two characters? Perhaps, Julia could be a bit aloof about were she was going?
- "she saw a large gray dog" might be changed to "She had seen" (easy mistake to make:)
- The conflict was resolved quite quickly in the ending of this story. It would make the story more interesting if the solution was not as easy as calling the Humane Society. Perhaps there could be a bit more mystery to the dog. Who are the owners? Why was he tied to the tree? These are the type of questions any young detective would want to ask. I'd love to read about Julia struggling with the right way to resolve some of these and maybe in the end, she could have a new friend to sniff out her mysteries with.
Keep up the writing...this is a really fun genre and I think you have a great character to work with.