Both DSs have had school residentials at about the same age. They went for 4 days and did outdoorsy things, although nothing as exciting as surfing and mountain climbing! They are both quite sporty though and have never had a problem being away overnight and had done a few camps with Beavers by that point, as well as staying with their Nanny a reasonable amount. There were some kids who were a nervous wreck on the morning they left, but tbh they were the kids who walked into the room al excited, then their mums started sobbing about how they would miss them so it got the DC all agitated. When they got back those same nervous kids were the last off the bus and were sobbing because they didn't want to go home!
I know it is hard to detach when they are that age, and i do agree that 4 nights is quite long for a first trip away from home ever, but I do believe it does them good to learn a bit of independence and to realise how much you do for them when suddenly you aren't there. It can be a great confidence builder as they come back full of all the things they have achieved all on their own (poor teachers never seem to get any credit) and in the case of DS2s cohort, there were significantly less problems with the groups of girls being spiteful to each other after their trip as it was exhausting for them to try and keep it up that long, so they saw how pointless the constant bickering was.
Is it possible that part of your daughters anxiety about going is due to her picking up your nervousness? I don't mean that to sound nasty or that you are upsetting her as obviously if you have never been apart before, it will be a big adjustment for you, but kids are very intuitive and if they think mum is upset then they figure it must be because of something scary and get upset themselves. It might help her feel more reassured if you try to brazen it out, sort of 'fake it 'til you make it' sort of thing, and focus on all the amazing experiences she will get to have, rather than the being apart aspect.
I have to say I do think it would be best if she went, not least because there was only one child who didn't go to DS2s school trip and he had a miserable week stuck with the older kids as his whole year was gone and felt really left out when they came back and were all that much closer and were doing work based on what they had done while they were away, so based on that I wouldn't like my child to be the one left behind, but you know your daughter best and if you really think she would be more miserable by being away from you than by being the only one going, then there is no shame in backing out and explaining to the teacher that she just isn't ready to be away for that length of time.