A baby in a pram can be covered with blankets I'm guessing your 9 month old isn't in an actual pram though. She needs a coat for properly cold days. Remember a child in a pushchair will get colder than you! You're walking and pushing them. They're not moving!
I think a proper coat if you are actually outside a lot, but I feel so sorry for little ones crammed in pushchairs/pram, with hats, coats, gloves, blankets and the like when you see them in a shopping centre looking like boiled pixies!
How about a thick lightly padded cardigan? There are lots about, then you can add the gilet and blankets as needed. DD spent lots of time like this with a hat on as well and unless we were out for a long time or it was particularly cold she was usually plenty warm enough. Layers are key I found.
We have used star wraps for my DS, he's 17 months now and are on the last size. They are not warm enough for outdoors in winter, we use his for bed and have to put extra blankets on him too or he wakes up cold.
They are quite thin, especially after a few washes.
I always found mine just needed a thicker fleece onesie (go a size or 2 up) over their normal clothes plus hat, mittens and footmuff and Pram hood up in our fairly mild winters. I did have a warmer coats/snowsuits for them but rarely used it other than super cold days. Jojo maman bébé do good fleece onesies.
Once they walk around I buy proper coats as they are more exposed but also better able to move in them. I only put them in snowsuits maybe 2/3 times per year in this country.
I also hate over wrapped babies in prams that must be sweating and can’t move. Although to be honest mine were mostly in slings so had body heat and my coat wrapped round them too if need be.