I think this is an interesting question because the size of the ship would cause all sorts of issues logistically, how you would support it, crew it and support it. How deep the water would need to be, how maneuverable it could be and if there would be special ports to berth it. Just building and launching it would pose all sorts of story building issues. The question of power and speed seems relevant to all of the above.
There are several things to consider. 1. Drag from the water. This is typically dependent on hull area in contact with the water. This increases with velocity. 2. The length of the ship. This is because you lose energy generating a bow wave pushing water out in front of the ship and also a wake behind the ship. In the worse case the bow wave and wake constructively interfere for a certain speed and the energy loss is maximized at that speed. For heavy ships with limited propulsion this is the limiting factor. 3. The number of screws and how fast you can turn them. The number of blades and and shape of the blades matter some but ultimately cavitation becomes limiting (and can also erode the material of the propeller). Up to a point, you can increase the number of screws and increase the speed. 308
A larger screw generates more thrust, but the larger radius means the linear velocity of the tip is moving faster and result in earlier cavitation.
The good news is that longer ships have higher top speeds, and that this effect dominates over the drag. Although having a clean hull or a dirty hull can still make a big difference of several knots. A 1 km long ship is about 3 times as long as a modern aircraft carrier, but you may want to think carefully about the width.
I think with point number 3, if you keep the aspect ratio the same you can have more screws for more propulsion. Although this might also be limited by the size and number of nuclear reactors you want to have. One per screw? So then you have all kinds of engineering complexity as to how you would coordinate the different reactors, what you would do if one reactor magical or nuclear had a problem etc. Other aspects of engineering plant could also be more limiting than just raw power. The shaft has to withstand the torque, usually there are reduction gears etc.
If you make the vessel more needle like then there may be some structural issues with what happens in heavy weather. Since depending you could have several wavelengths of wave under the ship. That would stress the hull. For a short boat you can ride the wave. For the very long boat you could be supported by two or more waves with sections of the boat being under a lot of compressive stress or tension depending on if supported at the ends or in the middle. This would ultimately become a strength of materials issue.
The choice of nuclear power or similar power density is probably necessary. The speed you want to achieve of 45 knots is higher than the published top speeds of US aircraft carriers. In general though as long as a carrier can move fast enough to launch airplanes, about 30 knots, there is not a lot of incentive for them to go that much faster.
The simplest calculation you can do, is to calculate the hull speed. The hull speed formula is the velocity in knots is 1.34 times the square root the length of the waterline. If you use that formula and the published length of a modern carrier (longer than the waterline length) you get about 44 knots. A more accurate way would be to calculate the <PERSON> number.
So if you are worried just about speed and you can hand wave enough power, and perhaps some cavitation suppressors, I think you can probably get to your 45 knots. You can also play around with some different ways to minimize drag with anti fouling paint or special magical coatings. 308