Different people view things differently and whether you are a risk taker or more risk averse, it's not wrong, it's just the way you feel. I lived in Singapore 3 times for a total of 9 years (twice before dcs and once after, dd2 was born there and dd1 was 3 when we moved).
I love moving but I do find that fore warned is fore armed and make sure I know lots about a place before I go. Flying with kids is fine, you'll get though it. Use the movies in flight, load up an iplayer with movies and games for your 3yo, make it into an adventure for her. We told our 3yo that she could swim outside every day and that was the big draw for her. We spent a while looking at Singapore online, the places we could visit and we made a list. We also took photos of her friends with us so we could look at them and talk about them when we got there. We didn't really skype anyone once we were there, within 2 months she couldn't remember who they were! Kids (even the change averse ones) are much much more resilient than we give them credit for. Whichever nursery or school she goes into in Singapore, they will have seen it all before and helped thousands of expat kids settle in. Remember too that she will take her cues from you so if you can be more positive, it will make it easier for her.
Will your mum or your friends visit at all? Singapore is a brilliant place for visitors, there's so much to do and see, public transport is excellent and of course no language barrier. So easy to get to Thailand, Malaysia, Indonesia etc too. Skype is so easy to use, will your mum do this?
Find some groups online for when you get there. This one is great for mums of under 5s and there will always be someone hanging by the pool to chat to. Find facebook groups. Do you know where you want to live? Where your dh will work? Schools for your dd? If you get planning, it will all start to feel a bit more real and a bit less scary. I haven't been scared about a move but I haven't met anyone who wishes they haven't moved....