A few thoughts here.
First, the Traveller dTon is a measurement of volume, not of mass. A 1000 dTon ship may easily mass more than 1000 metric tons, probably more like between 2000 to 3000 metric tons, unless it is armored, in which case it is going be weight quite a bit more. That is the mass that needs to be accelerated.
Second, if you are using fusion reaction drives, you are running into problems with the rocket equation, Final Velocity = Exhaust Velocity times (initial mass divided by final mass) to the Base E.
https://spaceflightsystems.grc.nasa.gov/education/rocket/rktpow.html
Assuming the ratio of your initial mass to final mass is 9 or there about, you will get a final velocity of about 2 times the exhaust velocity, which if I remember correctly from Maxwell Hunter's
Thrust into Space, will be somewhere between 3.1 and 4 Million Feet per Second, or somewhere in the vicinity of 1500 miles per second. That is well short of 0.9 C, not even 1 per cent of C.
Third, if you assume a reactionless maneuver drive run from your power plant, then you are looking at how do you handle all of the heat that the power plant is going to generate. You also have the problem of carrying enough fuel to achieve a decent percentage of the speed of light. Complete fusion of 57 grams of Deuterium will give you about 3 kiloton equivalents of energy. Fifty-seven kilograms of Deuterium will give you 3 Megaton equivalents of energy. Fifty-seven Metric Tons of Deuterium will give you 3 Gigaton equivalents of energy. That does assume that your power plant and maneuver drive is 100% efficient at using the fusion energy. If it is only 99% efficient, then you have around 30 Megatons of energy to deal with and get rid off, from your ship's power plant and maneuver drive. For comparison, that is twice the energy of the largest US nuclear test, the Castle Bravo shot of 15 Megatons.
The idea of throwing rocks as nuclear weapon equivalents is featured in Heinlein's
The Moon is a Harsh Mistress, but I think that his 100 ton rocks were only about the equivalent of 10 kilotons or so. I am relying on my memory for that, so I could be off, but the rocks were relying on Earth's gravity well to supply a large portion of the velocity, not the rock thrower.
Note, the following is the energy equivalent of 1 Kiloton of TNT. It is taken from
The Effects of Nuclear Weapons-1977 Edition. You can download it at archive.org to check my figures.
Complete fission of 0.057 kg (57 grams or 2 ounces) fissionable material
Fission of 1.45 x 10 to the 25 nuclei
10 to the 12 calories
2.6 x 10 to the 25 million electron volts
4.48 x 10 to the 19 ergs (4.18 x 10 to the 12 joules)
1.16 x 10 to the 6 kilowatt-hours
3.97 x 10 to the 9 British thermal units
Since a Kiloton is equal to 1.16 Million Kilowatt-hours, a Gigaton is going to be the equivalent of 1.16 Trillion Kilowatt-hours. For those used to metric units, a British Thermal Unit is the amount of energy needed to raise the temperature of 1 pound of water 1 degree Fahrenheit. One kiloton of energy will raise the temperature of 3.97 Billion Pounds of Water by 1 degree Fahrenheit. A Megaton will raise the temperature of that much water by One Thousand Degrees Fahrenheit. That is the heat load you have to deal with.