There is no difference in the cost of a right of abode certificate for British citizens and others with the right of abode in the UK.

As to collection of the passport, if the passport is being couriered/posted, then the question is who can sign for it. Normally the post office (and other, specialist couriers) will allow a person at the same address to sign for a parcel, particularly if the named recipient has signed a letter (or sometimes a special form) authorising this. You could check with Australia Post, but I don't know whether special rules can apply.

However, getting the passport to your sister is also a potential problem. Sending a passport by international post might be illegal and certainly must risk it being lost, although in practice I suppose the chances that it will arrive safely must be greater than not.

She could apply: she might be lucky and find that the passport is issued in time... Or if she is only planning to work in the UK and not in the rest of Europe, she can apply for a certificate of entitlement to the right of abode.

Of course, as noted above, she can apply for a British passport anywhere, including after arrival in the UK, but the question of referees and so on will be harder for her then. However, she might know people that fulfil the criteria in Britain...