I am so glad that your concern is for your sweet cuddly nine month old daughter rather than yourself. She is feeling the tension right now and that may be one reason she wakes up and wants to be assured you are close by.
I see no reason to worry about any kind of training until you are completely recovered. Do you think it would be safe to have her sleep with you and your husband while you are getting your complete rest post surgery? This makes the most sense to me. Your daughter will be relaxed and comforted and you will not have to do any lifting. She will feel safe and you will know she is happy and safe beside you.
In primitive societies it was natural for babies to sleep with mommy and we have gotten away from that although I know of very happy families where they have a family bed for the first years of their childrens' lives and these chldren thrive !!
Maybe during the first days of your recovery, she may need to sleep on daddy's side, but she is very attached to mommy right now and will be for a few more months so it is good that you will be in bed a lot where she can crawl, cuddle, be read to and feel safe and not abandoned while you recover.
As you get better and up more she can feel safe to go into other areas. It is not the case that when you hold a child close as long as that is what the child needs, the child will always want to sleep with you, sit on your lap, play by your side, etc. Actually having basic needs met and feeling safe and comfortable, the child is more willing to explore the wider world. And when she starts to walk and run and go farther from you, I hope you will be strong and able to run after her.
It is actually fortunate that you will be on bed rest at a time when she will be content to be there with you and picking her up is not an issue.
I remember taking care of a sweet one year old while her mommy was in an ankle cast and told not to lift her child. The child was so frightened that her mommy would not pick her up and didn't want anyone else to do so.
great grandma N.