If he's under 135cm it's actually illegal for him not to have one. Whether you'd actually get picked up on this is another question, but it has been made law for a reason - seatbelts tend not to fit children well below this height, which can cause a pattern of injury known as "seatbelt syndrome" - you can google this if you like, essentially internal bleeding and abdominal injuries. They can also "submarine" under the belt if they are slouching, which can be even worse.
It could just be a booster cushion, indeed. He's likely to be tall enough that the shoulder belt will fit him well enough on one of those. However if you ever do properly long drives where he might fall asleep, or you just want the side impact protection, he'd be better off with a full sized one. If you do this I'd go for a really tall one so that you'll get your money's worth!
We now live somewhere it's 150cm, so I do know the feeling - DS1 was badgering me to measure him every day and gleefully refused to use the car seat as soon as he reached that height! But we'd travelled to the UK a couple of years before when he was just 135cm, and I found he was OK in some cars without the booster seat, whereas in other cars he really didn't fit the seatbelt properly without one. By 150cm he really fits fine in all cars in all seatbelts.
What you could do is sit him in the car without a booster seat and assess where the seatbelt sits across him. You're looking for these points:
- Shoulder belt should cross his collarbone and not rub his neck
- Lap belt should cross his hips or thighs, not the soft abdomen
As a third point to note, you want him to sit in a natural and comfortable way, which means that he should bend his legs over the edge of the chair. If this causes his bum to be further forward than the seat crease, it will likely push the belt up onto his tummy and neck, even if it fits correctly when he's sitting back. He should also slouch in the way he would over time in the car for a proper measurement - otherwise, the belt might fit him well in your test but as soon as you actually get into the car and drive any distance, it won't be fitting him properly any more. That's not only more risky if you crashed, it's also less comfortable for him, so he might be tempted to do things like put the seatbelt under his arm (which is really dangerous!)
IME when DS1 was 135cm tall, his legs were just a bit too short to bend over the edge in most cars, so he most definitely scooted/slouched forward and that caused the rest of the belt to fit incorrectly. So the poor kid was destined to a booster for another 15cm, but at least I knew he was safe and comfortable!