We split ours all up for kidding, but you can leave them together, especially if they have plenty to room to get a bit of space from the others. The reason we split ours up is so that we can moniter what mum is eating, both before and after kidding. Want to make sure she is getting food, and we like to give them more fibre, veg and stuff. And that means the other don't steal it. But either way works.
I would have calcium on standby, just as in case. Remember that goats show signs of calcium deficiency by NOT sitting down, the opposite to a cow which will go down and not be able to get up. They seem to know if they are calcium deficient that if they lie down they may not be able to get back up, so just stand up. I'd also keep a syringe and needle, in case you need to give them some calcium.
A bottle and a teat- you never know if mum will have enough milk, if the kid will be strong enough to stand and suck. A kid might not be weak enough to need to be tubed, but might need the benefit of a wee drop in a bottle.
We have "goat towels", ie towels which are no longer good enough for the house but get used for the animals. Might be handy to wipe your hands on, and also to help dry up kids although straw is very effective as well.
We give mum a gruel of porridge oats, hot water and treacle or molasses straight after kidding to help them replace fluids and to give them a sugar boost, so you might want to think about having some of that handy.
Might be an idea to have a heat lamp handy- we tend to just take them into the house if they get too chilled, but we hand rear our kids.
A collar and lead- don't know if you'll have anyone else with you, but if you need to help her kid and she doesn't want you to, and you have no-one with you to help, you might want to tie her up.
I can't think of anything else right now, but if I do, I'll add it here!
Interestingly, I associate the smell of dettol with newborn kids. It's because my mum is a vet, so whenever she would go out to kid the goats with a bucket of hot soapy water with dettol in, kids would be along not long afterwards! So as a child, that's really what I associated the smell with.
Beth