Oh man, have I been there. It is hard to navigate the gift getting aspect of being a new parent. When my DD1 was 6 months old my mom bought her this:
It wasn't a holiday, she just bought it for no reason and boy was I pissed. How dare she buy this big, giant plastic toy for my house without getting an ok from me first. I had lots of arguments - DD was too young for it, it was really big and took up a lot of space, how did she know we didn't already have it, etc. I didn't even bring up the plastic argument because frankly that is so far off my mainstream family's radar they would never get. My mom was really hurt and upset, she was coming at it from the angle of I just wanted to buy my grandchild a toy, why can't I buy my grandchild a toy. The toy came out of a place of love, just like the baby alive doll did for your MIL and I can totally see how she would be crushed by your rejection.
I've changed a lot over the years - when my DD1 was 2 we got her a play kitchen and play food, I wanted to make sure she got a wooden kitchen and I made all her food myself from felt and also bought her some Haba and Plan toys food to go with it. Over the years my ILs have added some Melissa and Doug wooden food to her kitchen set, it is not what I would have chosen, but it wasn't cheap plastic food and DD loves it. Well, now my DD1 is 4.5 and my DD2 is 8 months and we just celebrated Christmas with some friends. And what did one of our dear friends get DD1? Yup, a big plastic barrel full of cheap plastic food from Walmart. And I smiled gracefully and accepted it and it is now mixed in with my DD1's kitchen set because you know what? The relationship is more important than the toy. In 20 years DD1 is going to remember having fun times with this friend, not that she had a plastic hot dog in her toy kitchen.
In your case, the damage has already been done so now you have to decide how to proceed from here. You could call up your MIL and tell her you've thought things over a bit more, feel really badly about what you said about the toy and you'd love to have it. You could go at it from an inappropriate age perspective and tell her she can give DD the doll for Christmas but then take it back to her house to store until she is older since you don't have the space. You could tell her all the reasons why you don't want DD to have this particular doll and point her in the direction of what kind of dolls would be ok. You could accept the gift, take out the batteries and take away the chokeable parts and have it just be a doll.
Advice for the future - have natural toy catalogs sent to MILs house, talk about what you are getting her and why and just accept all gifts gracefully and deal with it later. Over the years we've gotten a lot of gifts I would never have purchased for my kids, some have turned out to be her favorites, some have been played with for a day and neglected for years, but none have irrevocably harmed them.
Here is my pet peeve about giving gifts to kids - why does the gift have to be a surprise for the parents too? If your MIL wanted to buy your DD a baby doll, why couldn't she have called you and said I was thinking about getting DD a baby doll for Christmas, how about this one? Or did you have any ones in mind?
In this day and age of technology, how hard is it to send an email, text message, or call from your cell phone? Last week my Mom bought DD a pillow pet. DD has been talking about getting a ladybug pillow pet for months, my mom bought her a panda one. So when DD got the panda she was disappointed and reacted as so. Both my mom and my DD were upset. It all could have been avoided with a simple phone call. We've also gotten so many duplicate gifts - books, games, etc. for the same reason. Just call me, text me, etc. But for whatever reason it never happens.