Your DH has some scientific basis as vitamin A is fat soluble. BUT if she is also drinking lots of milk, and with a baby at pretty much the same time as the food, then she will be getting the fat she needs from that.
However, you do also need to look at your thoughts about nutrition as even in the UK the guidance for young children is different for that for adults. Some butter sounds okay, sugar though shouldn't be needed.
I wouldn't add it. It's not their main source of nutrition until one and unless you want to be carrying butter everywhere for years it's best to let them learn to eat things as they naturally taste. The fat will come from formula or greasy milk cheese , nut butters, avocado etc.