How many years into the game are you to design and build something on that scale? Good to have aspirations...
I'm just a couple years shy of the 150 year mark. However, I'm sure you could do it much faster if you were better at, and more dedicated to, managing things effectively than I am (probably at least 50 years faster). I don't think it was a conventional start or anything either.
Also, update: I finally fueled it and filled the magazines by gathering together the stores of many of my colonies and fuel harvesters. I think this thing is going to see limited use, however, given how much fuel it eats (and I have a couple 300k ton ships which are probably equally invincible).
Edit:
This ship seems to be worth it so far. The aliens brought up 30 FACs which each shot 20 missiles (like they did last time). 122 were taken down by the vast numbers of lasers that the fleet carries, and 477 impacted the Yesu's shields. Luckily, it has 6000 shields, so it was totally fine, and my navy has sailed through their attack completely unscathed. Hurrah!