Actually, this is not something you can do as a therapist or a hygienist according to the GDC. The GDC's "scope of practice" document states that only dentists are allowed to administer non surgical cosmetic injectables as an additional skill. This means that the GDC recognises this as a skill of a dentist and wont take action against them if they undertake this task while identifying themselves as a dentist.
However, that being said, there is no legislation in the UK that prevents a non medically qualified person from carrying out botox or filler treatments. So, Jodes may be able to provide botox and fillers, but she must not identify herself as a dental nurse when doing so, as this is not part of a dental nurses scope of practice.
You are also correct in saying that botox is a prescribed medication, but fillers are not. If jodes was correctly insured to provide botox treatment then it would need to be prescribed by either a dentist, doctor or nurse prescriber first.
Also, once you have your NMC registration, yes you will be profesionally responsible for administering any drugs that you are told to, but you are not yet responsible for prescribing. For you to administer botox you would also have to have either a dentist, doctor or a nurse prescriber clinically examine the client first and then allow the botox to be administered by yourself.