You're looking at around six hours of work, including shopping and clean up, but not counting commute.
The only sane way to bill a dinner for two is for the client to cover all expenses, while you charge a fee for your services (including transportation), roughly based on your time but with a minimum. As a recent graduate, not terribly experienced, but professional, I think a service fee of $150 would be about right.
The major expenses in your menu are the filet, scallops and two bottles of wine (which you should offer to purchase), assuming you use Choice meat, a reasonable, crisp Pinot Grigio, and a big, respectable red, you're looking at around $60.
That probably puts the meal in the $250 range -- which is also about right for a romantic dinner served at home. This is less than Pete would charge, but with respect to both of you, as a chef you're a little less than Pete at this stage of your respective careers.
Bring your own knives and any other specialty equipment you may want -- including stupid things you rely on like your favorite spatula or melon baller. Don't assume the client has anything in the home beyond a carton of peach yogurt with mold on it.
Ask about cookware. If all (s)he has is lightweight aluminum non-stick, you have to bring your own and you'll have to charge extra. Ask about cutting boards, too. Lots of homes have nothing but knife-wreckers.
I'm not sure what the client specified, but if it's an open subject there are something like a billion variations on filet mignon which include neither mushrooms nor Bernaise. I won't want to waste our time discussing any of them without an invitation. If the client supplied the menu, cook the menu.
Scallops served on the shell WAS passe, but now it's charmingly retro and back. Knock yourself out.
Don't forget to bring up the subjects of a pre-dinner cocktail and an after dinner drink. It's good to have those things nailed down in advance, you want as little improvisation as possible. The client should provide all hard liquor and special mixers (like bitters or Vermouth but not soda) unless otherwise agreed. Also, don't forget coffee (or tea) service.
Same food for both, unless otherwise agreed.