First things first, a lot of these dates don't make sense. I believe Mouse, and by extension Carrie, graduated in 1985, thus she would start college in the fall. So it would take a year or at least a couple of months for Carrie to meet Miranda for these dates to make sense. And how is Miranda starting in 1985 but graduating in 1990? Just a quick google search says that it would take three years to receive a standard degree from Harvard Law. So why is it taking 4-5 years for her to graduate? Did she need a couple more years? Did she pursue more degrees that thus needed more time? Would the third season have some kind of time skip to like 1987 and have Miranda and Mouse be sophomores? What this tells me is that there's actually no way for Carrie to meet Miranda as a Freshman and have her graduate in 1990. So I'm inclined to treat these dates as irrelevant.
Disregarding dates, what is Miranda like at this point? I don't think her personality would change too much. Kind of like how Carrie kept her idealism and romanticism, and Samantha kept her promiscuity and independence, Miranda would probably still be cynical and pessimistic. I'm willing to chalk this up to her Philly upbringing. I'm also inclined to think that her and Mouse would not get along, at least initially. I can see Mouse's ambition and competitiveness clashing with Miranda's demeanor. Hell, Mouse would probably see her as a rival anyway. It's just more fun that way.
This would also make for some really good conflict in regards to both of their friendships with Carrie. As mentioned before, Carrie meets Miranda crying in a department store dressing room. There are a lot of reasons why this could've happened. What we know of Miranda during this period is that she was pretty masculine and abrasive, so maybe she went to a department store only to be fiercely judged by a rude sales rep, thus reducing her to tears. Maybe she went there to get something nice to impress a guy she liked and that's what made her emotional. Or maybe both happened. Either way, this meeting is way too cute to disregard, so I would stick with it.
What would make this interesting is maybe this exchange happened before Carrie knew that Miranda was Mouse's roommate. I'd imagine Mouse and Carrie remained in contact, so she would always be telling Carrie how awful and rude her roommate was. So when she does find out that the girl she met at the department store is this awful roommate Mouse has been talking about, she's confused because this Miranda is actually very nice and the connection is instant. Then comes some kind of situation where Mouse and Miranda make Carrie "choose" who she wants to be friends with, only for Carrie to decide she wants to be friends with both of them.
Of course, Mouse and Miranda get along in time. First they're cordial to each other, for Carrie's sake. And then maybe something happens that brings them together. If I'm writing the episode, here's how I'm doing it: Mouse wants to go out with a guy, Miranda tells her he's no good and she's only looking out for her best interests, Mouse tells her to piss off because they're not friends, said guy hurts Mouse in some capacity, Miranda stands up to the guy for being a jerk and says that Mouse is too good for him anyway, Miranda concedes to Mouse she actually does care about her, Mouse realizes she misjudged Miranda, and they become friends. Bring on the ending scene with Mouse and Miranda sitting on a bed together eating and laughing.
Add in some more stuff about Mouse and Miranda's relationship, her time at Harvard, and her getting to know some of Carrie's other friends (i.e. Samantha), you pretty much have Miranda's part in the series.
The big question is what happens to Mouse and Carrie in the time between this period and the SATC universe? Why is it that Miranda and Carrie stay friends but Mouse and Carrie do not? I don't have an answer to this, but I'm inclined to think it's just a matter of people drifting apart. Maybe after graduation Mouse gets a job at another part of the country and doesn't keep in touch with Carrie, whereas Miranda moves to New York and stays with Carrie. But that's another discussion for another day.
So yeah that's basically all of my thoughts on the matter! This is kinda longer than it needs to be, but I just have way too many feelings about Miranda Hobbes and The Carrie Diaries. And yes, I am mad that The Carrie Diaries doesn't get a third season, so this situation and thus Miranda's part in the show is theoretical. But it's fun to think about.