Yes that is a tick, if it is the cause of your DD's temperature then she definitely needs to see a Dr. But if it isn't the cause, and is just a coincidence, then she still needs to see a Dr because a temperature of 40°C that has not come down after having Calpol, needs investigating anyway! If the Dr finds redness in her ears, and/or throat, and/or swollen glands, then s/he may well say to just keep her fluids up and continue to give her Calpol.
If the Dr can't find an Immediate cause s/he should listen to her chest and heart, and if s/he still can't find any other causes, then imo the Dr would be very stupid to not give her antibiotics, as it seems like the tick could indeed be the culprit. Can you maybe give your DD a tepid bath, and check her thoroughly for any other ticks whilst doing so.
I have very strong feelings against prescribing antibiotics unless they are definitely needed, but in the case of your DD I think that the presence of the tick does warrant the Dr giving your DD antibiotics anyway, even if s/he has found her to "just" have what s/he considers to be a viral infection. As a PP said, if Lyme disease gets hold in someone's body it can be very nasty.
If you come away from the Dr's without a prescription for your DD, please keep a very close eye on her, and if there is no improvement within a few days, or if she gets worse, please take her back to the Dr's, or even to A&E of course if she gets much worse.
By the way OP, does your family have a dog, or any other animals that go outside, or does your DD enjoy rolling around in long grass - or even walking or running through vegetation? If so, that is of course lovely, so please don't stop her, but if you could get into the habit of checking her over when she comes in after such activities, and also checking over any pets, then hopefully the horrible critters won't be given board and lodgings on your DD again, or on any DPets.
Oh by the way, it might be a good idea to go into your nearest vets or pet shop and buy a tick remover - mine looks a bit like a minute green fork, then look up on YouTube how to remove ticks from the skin of any animal, including humans. It is a long time since I had to remove one from my dog, but I think once the 'fork' is in position you give it a good twist - to break the ticks legs I think - so that you can get the whole thing out, not just it's swollen body! Did you notice whether the one you removed appeared intact, head/body and 8 tiny legs?
Just as an aside, my DH and I always let our DDog sleep on our bed, but the time I saw a tick doing a 'quick' shuffle towards me on the sheet beside me, nearly gave me a heart attack - well it at least gave me a revolting shock! DDog still sleeps on our bed though🕷🤭
They are members of the wider arachnid family, but maybe don't tell your DD that!