To give a sense of the scale of the beginning of true outer space: the nearest star system, the Proxima Centauri system, is 4.246 light years distant, or about 269,000 times the distance from Terra to the Sun. For comparison, Pluto is only 40 times as far from the Sun as Terra.
Our galaxy, the Milky Way galaxy, is over 100,000 light years across, that's more than 23,000 times the distance to Proxima Centauri. This is the scale of true outer space, galactic space.
The QRJ will act as a kind of ‘warp field/shield’ which protects the ship from the effects of these speeds such as time dilation.
Hyperspace is a technical term that means more than 3 dimensions.