My DS was present at my homebirth with my DD. He was 4.5years old at the time. The only other people present were my DH and the midwife.
We had told DS about birth earlier, explained there might be some weird noises but it was okay and Mum wasn't sick - just that it was a bit sore to get the baby out. We explained that there might be a bit of blood, but it was okay too, that's what happened when the baby came out and that there was nothing to be worried about. We told him he could come into the bedroom or watch his movies in the lounge - or come back and forth - whatever he wanted to do.
I was in labour during the day, nothing major and manageable. While I was coping, we didn't say anything to him. When it became more intense, we got heaps of snacks out for him and told him the baby was getting ready to come. He just kind of shrugged and went back to his dinosaur movie. I was in active labour for 2 hours and 45 minutes and over that time he just wandered back and forth between the lounge and bedroom. When I got a bit noisy, he sat up by my head and patted my hair and offered me his drink bottle. He was there when she was born, he looked down and said "ewwww, she's slimy". When the cord was being cut he asked why - we explained it was how the baby was fed on the inside, but she didn't need it any more. He thought about it for a moment and said "Yeah, and anyway, you'd have to cut it because if you wanted to ride a bicycle, she'd be bouncing along the road beside you". Made me crack up - and I realised that he because he knew there was nothing "wrong", he was very unfazed by the whole process. Then he went back to his movie.
He is now 13 and DD is 8 and we're planning a homebirth for No.3, due in 10 weeks. Both will be here and both can choose to come and go into the room if they please. DD is adamant she wants to be woken up if it's in the middle of the night, DS just shrugs and says whatever.
It seems your LO is over 4, so if it's explained very matter of factly (and they are not an extremely sensitive child), they will probably do fine being there.
You don't need much for a homebirth - they don't tend to confirm them til later in pregnancy anyway to make sure you haven't had complications that would preclude your eligibility. 36 weeks will still leave you plenty of time to get organised. I had such a great experience last time, and I have relatively uncomplicated and fast births, it was a no-brainer to do it again.
All the best!