jacksoo, welcome to AFF.
Upfront, none of the following is intended to exonerate Webjet in any way.
First, I assume you did not (or couldn't possibly) make a mistake when entering your names into the booking process. Apart from that, I would have also attempted to check the underlying e-ticket (e.g. if it was issued using Qantas ticket stock, then you could go to checkmytrip.com with the Qantas reference to check the ticket). If the names were incorrect there and you were sure that you didn't make a mistake entering your names in Webjet's engine, then you definitely have a case, albeit really unusual how it could manifest this way.
All said and done, $75 only would seem little pain relative to what they could do, e.g. refuse altogether the name change and/or force you to forfeit the ticket / pay fare difference. Then, you would have a much, much more difficult battle to fight.
As for the baggage, are your Brisbane - Hong Kong (Qantas, no u) and Hong Kong - London Heathrow flights connected? That is, you fly BNE-HKG then straight onto HKG-LHR (timing wise, this means a transit at Hong Kong airport of approximately six hours or so, if my memory of the timing serves me correctly).
Somewhat technically, Webjet are kind of correct. Assuming both of your flights are transit-connected, you would have the option when checking in at BNE to check your bags all the way to LHR. In this case, since the allowances of both carriers are different, the baggage allowance of the Most Significant Carrier (MSC, defined in IATA conventions) will apply. The MSC in this case is BA, so the BA baggage allowance (1 piece of no more than 23 kg) will apply when you check in at BNE.
However, if your flights are not connected and you have a stopover in Hong Kong, then you will likely only check your bags at BNE to HKG. In this case, it is possible to be accorded the QF allowance when you check in your bags going to HKG, and then the BA allowance when you check in your bags from HKG to LHR.
Still, if you had the six hour connection or so in Hong Kong, the two allowances may still apply if, for example, you go to HKG, claim your bags, take something out (e.g. a gift for someone), and then the resulting bag meets the onward carrier's allowance (BA in this case). For example, if you meet someone briefly for dinner and have something to give them. In that case, however, you would need to ask the staff in BNE to short check your bag to HKG so you can claim it there.
The previous two paragraphs are my understanding; I've been told in some cases the allowances have been marked on the tickets which may make the second of the two previous paragraphs difficult to work, or impossible.
What is not possible is for you to check your bag in BNE all the way to LHR (no claiming in HKG), and expect to have the QF allowance of 30 kg.
In the end, the agents cannot change your baggage allowance entitlement - it is up to the carrier. So unless the agent is the carrier (i.e. you bought the ticket on the airline's website), then baggage allowances should always be checked with the carrier.