Go for it! Ask her what takeaway she wants and have it arrive when she does so any awkward initial chit-chat is focused on the food and eating. Open the wine at the same time. After you've finished eating, the wine should have had some effect and you'll feel more relaxed. Make sure you agree on the film beforehand too. Get some nibbles and more wine to have during the film.
Glad you posted here otherwise they may have been very awkward moments leading up to 'who sleeps where'. She would absolutely not expect to share a bed with you - you're new friends and you're adults.
If she does, then just offer her the sofa.
Have some stuff you can make for breakfast and have a prearranged (real or not) event to go to the following day. Let her know about this before she comes round so she'll have to be gone by 10am, say.
You will feel uncomfortable at first - after all this is all very much out of your comfort zone but give it a go.
Conversation - the film you'll be watching is the first topic. Find out about the actors or theme, to fill gaps. Talk about your child. Have some anecdotes up your sleeve. Maybe she's a chatty person and you won't have to worry.
But please try and give it a go. I think you'll regret it if you don't. You may hate it all and never have to do anything like it again, or it may open up a whole new way of living and social opportunity for you. You may not have the chance again.