Yes, and even better, don't design the ring by yourself. Get a nice jewelry box for the diamond, use it for the proposal, and when you open the box, say:
"Our relationship is something we're going to build together. I want your opinion on everything for the rest of my life, because you're going to be my partner. I got the diamond, but let's design the ring together, you and I, because this is too important for me to do by myself. I need your help."
They'll melt, and the ring will mean even more.
You're supposed to know what kind of ring your soon-to-be fiancé wants ahead of time.
And they're going to want to be able to put it on their finger right away.
Usually people want to be able to put the ring on their finger (for pictures and engagement announcements) as soon as the question is popped.
Also, the "I need your help" line falls a bit flat to me. Reads like the proposer isn't capable of completing a very important task without some handholding from the "proposee".
Also theres not much to a high quality ring and not much for you to spend money on there.
You could also consider using a temporary ‘semi-set mount’ for the proposal. Then afterwards you could go to a jeweller and have them create the perfect ring to your specifications.
Now, 6 or 7 years my wife has a big birthday coming up and I’m considering a diamond pendant - when I bought the diamond for the engagement ring there was far fewer options but now there’s lots of places online. LooseGrownDiamond seems very competitive but if you find anywhere better priced I’d be interested!
I hear many jewelers are not big fans of this. It's like a customer who bought their own steak to a restaurant and asks the chefs to cook it at a discount. It's not like the jewelers don't know where to buy cheap stones online. Some jewelers are just happy to get the business, but expect others to sneer a bit.
Now gold is worth 2.5x what platinum is worth.
https://www.macrotrends.net/2541/platinum-prices-vs-gold-pri...
However, "retail" jewelry stores often price things using what they call Keystone (2x markup) or even triple keystone (3x). So, a $500 piece would sell for $1000-$1500.
Some women would honestly prefer a 0.5-1.0ct natural vs a 2.5ct synthetic.
In any case, the ring is for her, so I'd recommend making sure she's on board with what you're thinking.