Appreciate all of the feedback & comments. Sorry I'm not great at using the "reply with quote" function and I'd rather not create 20 individual replies, so I'll try and answer the questions / points here in one hit:
1. I messaged RedRoo on here first with the complaint, and they directed me to "customer care" so I doubt contacting them again will achieve much.
2. Prefer to travel as a family, which is why we didn't order 2 cars. It's always easier with an infant with 2 people. Plus we were staying at an Airbnb in Paris, not a hotel, so more likelihood of getting separated and lost. The website states they have vehicles to cater for special needs. The QF rep states that we didn't request a large car - it should go without saying if there are 3 passengers and that much luggage (that's all they asked, never asked us about car size).
3. Re: why we didn't change our daughter at check-in. There were several reasons. Firstly they said it would take 5 - 10 minutes. For the trouble it is to get her in & out of the pram we'd rather wait the 10 minutes (she's a wriggler!). Problem was it took far longer. We still had all of our luggage with us and my wife is loathe to leave it, especially when there's a huge pile of it. She didn't know where the bathroom was and would much rather use the lounge facilities than the public ones. And the main reason was the full extent of the "damage" wasn't revealed until we got her out of the pram - we thought she was tired.
4. Sorry, just to clear up - the MEL-DXB-CDG was through EK, the LHR-DXB-MEL was through QF. I'm not upset about the fact that I had to pay $82 - I'm upset about the fact that I only discovered this after being denied check-in and having to wait around an hour to find this out, with a screaming infant. Qantas acknowledge they stuffed up because they had numerous times to request the payment from me - I spoke to them a number of times via phone before the flight, including when I booked the flights, and I was never asked to pay anything.
5. Eastwest101 - thanks. We really did try - we're regular travelers and our main concern was getting through the flights with as little disruption as possible to the fellow travelers. I think we achieved this really well, it was the non-flight components that really mucked us around.
6. What PrincessFiona described regarding Dubai Connect is correct. We got the vouchers at check-in, but we were assured (as expected) that there would be heaps of ground staff around to direct us on where to go when we landed. Travelling in J, and with an infant in tow, we thought we'd receive pretty good service/instruction. It just didn't happen. We asked multiple people who had no idea, then when we got to the two queues for "transfers" or "immigration" the EK rep there incorrectly directed us to the transfers area. Unfortunately for those who have transited through DXB would know, by the time you get to this stage you've already done a 20 minute uncomfortable bus ride from your plane to the terminal which is a really poor experience to begin with.
I didn't have much time to research Dubai connect as I changed our flights the day before we left because there was a flight departing MEL at 9.30pm on an A380 instead of ~2am on a 777 and we thought Dubai connect would work well for us with an infant... how wrong we were.
Although EK had 3 "stuff ups" and Qantas had one, it was the Qantas one that affected our trip the most. With the CD issues we got there in the end. The Dubai connect process I guess is the same for everyone, we should have researched more but it should be easier and there should be staff around that can assist. The Qantas experience was a direct result of their stuff up, not charging me the correct fees at the time of booking and not picking it up in any of my interactions with them. And the impact, being at the start of a long journey, was huge.