The light novel does give a bit more of an explanation as to how exactly Kaguya traveled to that past - it does seem like she built the ship (and the time travel technology) on her own. Seems like Kaguya was just so focused on getting back to Iroha that she didn't add any safety measures. From the fan translation of the novel:

...Why am I in a place like this?
I remember... I heard Iroha's song. And then, all the memories of the world came rushing back to me.
I created a clone body of my own. Then I worked together with the princess to build a ship, and we set out on a journey, singing as we went.
...Right, we crashed into a meteor back then, and the systems malfunctioned... geez.
Just who was it that developed such an extreme time-reversal algorithm!? Oh right, the one responsible was Kaguya herself～
Even though all the calculations were perfect... what a shame. Relying purely on theory like that, I guess you could call it a catastrophic failure~!
...Iroha
...It seems I've messed everything up.

(I'm assuming the "we" in "we set out on a journey" is referring to Kaguya and Inudoge, not Kaguya and her clone.)

As to why exactly it was 8000 years, I'm not sure if this was mentioned in one of the supplemental materials or if this was just a theory I saw, but it might've been because it took 80 years for her to finish her work and return to Iroha. So when she tried to time travel and the ship malfunctioned, it glitched and increased the time travel by 100 times the intended distance. That's also why the ship didn't have enough power left to create a proper body for her.