Your DD will be fine and the sitter will be fine. The dress will be fine, the bit that won't is: being surrounded by people who are more glamorous/thin/well off than me and lack of time to psyched myself up for it - you are worried about yourself on the night, the rest is excuse making because you don't want to say you're scared.
Look, your DH loves you, there might be more glamorous, thin, better off people in the room, but you know what, you don't need them to think you're great, the only person in teh room who's opinion matters are your own and your DH's. He won't see this as an issue because to him it's not an issue.
This is a self confidence thing, and needing time to prepare for something that scares you. You can do it, it'll be fine. go on the understanding you can leave early, DH drive back so you can sleep in the car. it won't be as terrifying as you think - and not all the other woman will be thin, glamorous and rich, and even if they are, so what?! They won't be judging you. Only you will be judging you.
The more you run away from these situations, the harder you'll find them, it's your confidence that's the problem, not the lack of notice, or the day out or your DD's behaviour for a sitter, or the lack of dress (although that could help your confidence), it's that you are nervious. But it'll be fine, worse case situation, it'll be dull. Best, it'll be a fun night out with your DH. But it won't be people being rude to you and making you feel bad. Go, you might be really glad you did. and there might be more fat frumps than glamorous skinny minnies