Since you say she wants a big diamond, that is what she should get. You realize, of course, how big a carat rock is, don’t you? I suspect if she gets that ring, there will be times she will not wear it - say for gardening, under gloves, etc.
Make sure you know what cut (shape) she likes best. The traditional “round” diamond is not the only one. IME, diamonds of similar weight but dissimilar cuts can appear to be of vastly different size.
When I got engaged, I was in school, and I bought a .5 carat diamond. That was probably the most money I had spent on anything at that time. Now, 15 years later, I think I wish I had been a little more original. When a woman shows me an engagement ring, if it is just a diamond, my (unstated) response is, “ho-hum. Looks like any number I’ve seen before.” But if they have an opal, a black pearl, or something else I’m like, “Neat. Tell me the story behind that!” And I think that there must be something more to these folk who are strong enough to not submit to convention.
Don’t forget. You’ll (hopefully) have plenty of anniversaries to supplement her jewelry collection. So far I got my wife diamond studs, a 5-diamond 5th anniversary ring, a one-carat solataire at 10 years, etc… And she has several different wedding bands she wears: a fancy one welded to her engagement ring; a couple of plain gold bands for if she is gardening or something; a white gold one depending on what she is wearing; etc.
Final engagement ring observation. I recently overheard some younger female attorneys in my office discussing rings. It was amazing the distinction between the women who had gotten married while in school, and those who were anticipating getting engaged in the future. Those who were already married had relatively modest rings, whereas the working single attorneys really wanted ostentatious rocks. I was really stricken by the clear discrepancy between the two groups.
Good luck, and best wishes for a long and happy marriage.