Ah, if she's coming to live then that's different, sorry. I thought you meant for the weekend :)
I would in that case sit her in your car without a booster seat and see how the seatbelt fits on her. Between 135-150cm, it's very much about the build of the child and the size of the car seat and seatbelt.
You're looking for it being across her lap or hips rather than the soft tissue of her abdomen, for her knees to bend at the edge of the seat when her bum is right to the back of the seat (if they don't, she will naturally pull her hips forward to allow her knees to bend, which will make the lap and shoulder belt sit higher), and the shoulder belt to cross her collarbone and not irritate her neck.
If she doesn't meet any one of these criteria, then she would be safer with a booster seat.
You can still buy backless boosters, the difference now is that they are only approved for children over 22kg and 125cm which is about 6-7 years old. If she only needs a little boost and feels more comfortable or you don't want to spend a lot of money this is an option to improve the belt fit. But that is all that a backless booster does, just shifts the child up so that a seatbelt will fit them more correctly, it doesn't offer any actual protection in a crash.
If you wanted to spend a bit more money and/or she wants something more comfortable, and/or you're keen on the idea of her having side impact protection for her head as well, you should look at high backed boosters. However these are a bit trickier to buy for an older child because many of them simply don't extend high enough for their shoulders to fit under. So I would suggest that you find the biggest shop with plenty of high backed boosters on sale and take her to try and find the highest one which she also finds comfortable (it might even be fun?) It might not necessarily be the most expensive - the Britax Adventure is known to be a tall one and that is only £30.
One more note - children shorter than 150cm often can't reach the floor in a normal car with their feet especially when on a booster seat, which can cause their legs to fall asleep on long drives and encourage them to slouch. It's safe to put a box or something under her feet as a footrest for comfort for her.