Thanks for such a large response everyone, I've taken a while to digest it all. I'll confess it's all a bit more negative than I imagined, but some good points in there.
A bit of background info - I've taken months and months to think about whether to do the trip already, including all the research about passports, airlines, what help might be on offer, tips for flying with newborns, etc. Logistically I'm happy there won't be any insurmountable obstacles - I can get the passport in time (processing is quicker in NZ) and the airlines are actually super helpful, I'll get a bassinet and help with luggage. My midwife has also OK'd this trip.
And of course, with any major complications I just won't go, I'm booking fully refundable flights (like c-section, feeding problems, baby not well, etc.).
As for why I want to go - it's two fold. 1. I desperately want the chance to introduce my baby to my parents, siblings, aunties, uncles, cousins, etc. It's a free flight, I won't be able to afford to go otherwise (and none but my parents can afford to come out - and even then they can only manage Xmas time as they have their own business to run, which means no visit for almost a year minimum) and I have no family in NZ, they're all in the UK. 2. The conference is work related, but not actually through work. It's for a global organisation I belong to (kind of like a chartered association, but for procurement professionals) and I'm studying for the equivalent of a degree with them (on top of full time work). I ran for the position of student representative for all students in the Australasia region at the beginning of the year and won. It's a voluntary position, and other nominees missed out because I won. I'm taking the role really seriously, and have promised the region's students (there's thousands of them) that I'll take their issues to the conference, which is the one chance we get to try and change things for the better (there are lots of issues with the courses and exams). To have put all that effort in, to have worked so hard to set up a framework for the role and gather feedback, to have made those promises to other students, and to have taken the role off other very passionate and committed students - and then not go to the one big main event that the whole role is about - I just can't do it.
So, what I'm trying to manage is how to make the trip as smooth and stress-free as possible. I've spent months trying to develop a positive attitude about it, because I think if I'm afraid of the whole thing it'll make it impossible. My family will help out hugely when I'm there, and have all the baby stuff I could possibly need. If the expressing doesn't work out, yes, I can take baby in with me and feed in the conference I guess. I don't really think of my parents as strangers though - I am arriving a few days early to get everyone used to each other. I'm excited about them getting time with my baby! I do realise that I'm at a disadvantage not having done any of this before, but I'm sure it's do-able with the exception of issues large enough to stop me going anyway.