A couple of things right off of the bat. First, you have a nice funny story. The problem that I have with it is that it's taking too long to set up and the story is set too early with so much going on. Your what, 10 or 11 chapters in and you've not even got to a relevent chapter where Harry's school age? Not a good set up. You have grown adults following a 6 year old. My daughter will be six in March. This isn't a relevent age of anything, and you're portraying it as a relevent age. At six, surely Hermione could be prosecuted for not being about to see spot run, but you're putting an adult context to it that just doesn't fit. I can understand your Harry's character being more adult having that aspect of his life there for him, but Hermione didn't come from the future and certainly wouldn't be in that adult mindset. You're writing as if she tagged along and it's not believable. Next, like I started the story's moving too fast. You would have been more believable with a chapter that skipped for every year to school age and skipped every school year for every chapter. Instead, you're delaying, hoping that it makes up for it in content and while the content has been entertaining it hasn't matched with the age frames of the characters. You need to push along the interaction with Harry and Blaise, since that is where you're pushing with HER, and find a solution with that problem. Next you need to decide where you want your Weasley's. On the forefront, there needs to be a resolution with Severus, and he needs to be dealt with with utmost promptness, but you created the problem and now it needs to be resolved because without a resolution there's nothing that will be believable. He threw a killing curse toward an almost seven year old. It's not redeemable or for the greater good.
It's kind of like raping a seven year old. It's just something that you shouldn't do without immediate reprecussions. If you are allowing it, 1) your Dumbledore is truly dark or in advanced stages of Altzheimers and not DEMENTIA, and 2) you're making your Dumbledore a dupe in not questioning the acts of Severus 3) Dark!Dumbledore, which would make Harry more of a sympathizer than anything else. 4) Your Harry is already killing people anyhow and not thinking one way or the other about it so it's all ok anyhow.
The storyline and timeline needs work to make it believable. Too young for what is happening in real life. Too young for anything else of real substance to happen. Too young for the break from Azkaban but that happened anyhow.
Now, what are you going to do to fix this. I didn't think that your writing sucked but at the same point your time framing leaves a bit to be desired and to make it believable.
The worst thing about this story is the timing. It's not the writing. Had you picked a better timeframe for it to start you would have had a better believable more workable storyline to work with. I'd have suggested either the beginning of 4th year or the end of it. Go with a Dr. T model of it and worked with it. Now, at age six you have alot of relationships to build upon.
Now, with Mrs. Zabini taking that book from Nicholas, you have some catch up to play with before Blaise is no longer a love interest for Harry and at the same point if IT is still a love interest you have an ambiguous sexuality to deal with in either coming to terms with the sexual identity of a formal female at age six, where the character has already identified with being a female and Harry becoming GAY to help that interest, or you have a whole crew dealing with turning Blaise back to fulfill the interest. Also you have Harry admitting that there was a certain female problem from the future. Either way it's messed up.
I'd suggest a chapter transitioning through the next few years building the relationships but I doubt that will work. I do look forward to what you'll produce but I think it will be a hard road to sell.