The core things to ensure are:
Ensure the device is listed with the appropriate regulatory body (in the US, this would be "UL Listed", but this will vary in other countries). Typically this is explicitly on the label of the device, but you can, and should, also look up the device with the regulatory body (UL listings for example are here. Typically there's also contact information (UL has a phone number and email address) if you don't want to go through the hoops of getting an account etc.
Ensure the device is grounded (in the US, this means it has a 3 prong plug). This makes it much less likely the device will have an electric fault causing a fire or electrocution.
Ensure you have an outlet that will support the necessary amperage for the heater, ideally on a separate outlet (at least in the US). (This piece of advice may be a bit US centric, I know that European wiring is different and don't know enough to say if this applies there or not.). It's not required, but as space/floor heaters use a significant amount of power constantly, they're very likely to end up overloading circuits if they're on a shared circuit with other things. The safest choice is a single circuit just for the space heater's outlet. This will vary in some countries depending on how electrical wiring is typically done and what voltage is supported; contact a local electrician to make sure you're fine. Do not put it on the same circuit (not just meaning the same wall outlet, but any other outlet on the same circuit) as another device or devices that draw significant power (think a microwave, another heater, etc.).
Ensure the heater is located in safe location, that is not near anything at all - the heater will specify a radius that must be kept clear of anything, not just flammable things. Further, in a toddler's room, consider that odds are the toddler will find a way to put something flammable near it if at all possible! Consider keeping the room clear of anything that could be thrown near the heater - stuffed animals and blankets are the biggest risk here, though, and pretty hard to keep away from a toddler. Do your best.
Ensure you have working fire alarm and CO detectors in the room. Make sure they will alert you - many modern detectors can be interconnected so one going off will alarm the others. There's no way to be 100.0% fire safe, especially with electric heaters, so make sure you will know if one does happen.
Pick a heater that has a grating that is smaller than a child's smallest finger, or a style that has no need for a grating. Expect your child will find a way in to anything that can be gotten into.
Pick a heater that will not tip over - floor heaters can be "tippy" if they're too narrow/tall. Make sure it has a wide enough base that your child cannot tip it over.
There are some "nursery heaters" that are aimed at this market; I don't know anything about them, but they seem to have most of the heater-specific criteria covered at least. If the outside only gets down to 5ºC, you may be able to go with one of the less powerful options, which will make it much safer at least in terms of the electricity-related risks.
Also consider other options you can use to keep the room warm, including insulating the room (you can cover windows in plastic to add a few degrees' insulation, as those are often the worst offenders particularly if they're old single pane windows), and simply avoiding heating the room except when absolutely necessary - blankets and warm PJs do wonders, even down to 5ºC external temperature. If the house can hang out at 15ºC just with its insulation, you may be able to avoid running the heater nearly ever.