A transformer is a very simple device. It has a magnetically-susceptible core of iron, and wound around it are two coils of wire, with a ratio of 2 turns on one to 1 turn in the other for your purpose. The primary coil is connected to the input wires from the wall outlet to run on 120 VAC, and the secondary coil is connected to the output socket of the transformer to deliver 240 VAC to your computer cord. Could something go wrong with that? Of course - nothing is perfect. A unit like that might create voltage surges, for example. Or it may not include proper grounding.
In Canada, the electrical supply in the home uses what is called a "Grounded Neutral" system. That means that, at the wall outlet you plug into, the Neutral line actually is connected to true earth Ground back at the breaker panel, and the Hot line is not. This established a reference point electrically of zero voltage in the power supply system. But when you use a step-up transformer the output from the secondary winding is NOT connected to Ground, so the power being supplied to your computer has no connection to zero voltage through that. In itself, that is not a problem. However, sometimes one is dealing with other devices connected that are poorly designed and assume that a particular part of their circuit will be effectively at zero volts; if that is not the case, sometimes such devices can cause odd circuit loading and current flows. If your modified system lacks a proper Ground connection (next paragraph), that can happen and can even cause damage in some cases.
Our system here also has a third contact in the wall outlet, the round-shaped hole at the apex of the "triangular" arrangement of holes is for Ground. The power cord from wall to your appliance connects this line to the exterior chassis of the unit so it is at Ground (zero volts). This line is completely separate from the Neutral line and it is connected at the breaker panel to earth Ground. But it is a safety device and normally carries NO current - it is there mainly to provide a safe and low-resistance path to true Ground in an abnormal situation where the exterior of the appliance somehow makes contact with the Hot supply. This Ground connection will carry that dangerous current to Ground immediately, making the exterior still safe to people and at the same time causing the circuit to overload (a short circuit from Hot to exterior surface to Ground) and the breaker in the Hot line to trip open, stopping the supply of power. But that Ground connection also is used for another function. In equipment that may be disturbed by external electrical noise signals, this connection to true Ground with no regular current flowing through it is used as a good place to carry the noise signals to Ground and eliminate their effect on the circuits inside. So if you use some device between the wall outlet and your appliance (like the step-up transformer unit) that does NOT connect the wall Ground right through to the computer's Ground terminal on the power supply input, that function of noise removal is not possible.
IF you are using a Surge Protector device in your power lines that might cause another problem, especially if it is between the transformer and your computer. The simpler surge protectors (and hence less expensive) also are really simple. Typically they contain two MOV units, one each connected from the Hot line to Ground, and from Neutral to Ground. Such devices are built so that they are very high-resistance leaks of tiny current at low voltages, but at some specified high voltage (often, about 200 V) they break down and carry a very heavy current to prevent the line with power (Hot or Neutral) from going to too-high voltage with respect to true Ground. It causes a short circuit which usually trips out the wall supply circuit's breaker. If such an event occurs, two things could happen. IF your system does have proper connections to Ground, then the device works and prevents the voltage surge BUT this is a one-time thing! The MOV itself is destroyed in doing its job, and that might cause a failure of the entire surge protector unit afterwards. On the other hand, IF your system does NOT have a proper connection to Ground where the surge protector is connected, then it cannot do anything useful at all, and there is no surge protection.