Hey Boston,
Here is some advice worth considering. Especially consider buying just under the whole carat (e.g. .95 carats rather than 1.05 carats). You can always just tell folks it's one carat -- it rounds off to that. Also, buy slightly less than perfectly clear, etc., if your budget is a bit cramped. Again, without a jeweler's eyepiece, you won't be able to tell the difference (and maybe not even then). Also, small diamonds off to the side of the main diamond adds real opulence to the ring as a whole.
Finally, have you proposed? Are you planning on doing so with the ring? If not, I would strongly recommend going to pick out/purchase the ring with your fiance as a date event, with a nice dinner afterwards instead of going it alone. You're going to be a team in life. Start out that way unless you really think she would prefer you do this yourself.
Asking parents is a throwback sort of thing. Do it if you want, but if it seems inappropriate, don't worry about it. And if you do, make sure you include her mother in that event. It will do you zero good to have asked her dad and insulted her mom in the process. I shudder at the thought of it.
Best wishes,
Skillet