Deleted

You're looking at it like it's one decision ("should I take the job at Goldman while also moving cross-country and proposing at the same time to keep my girlfriend's emotional state as warm as possible"). In reality, there are multiple axes. Taking the job is its own question. Choosing to relocate is its own question. Proposing is a very distinct and separate question.

The extent you need to isolate each axis when making a complex decision depends entirely on how serious the consequences of that decision are.

So, let's look at your situation.

In order of seriousness, I'd say it's probably relocation, then job, then proposal.

One could argue the first two might be in the wrong order, but that's short-sighted. Relocating comes with merely a one-time financial and time expense. Career moves have a massive expense (or payoff) when you think of the compounding effect over duration. 

Relocation:

Do you care strongly about New York? Is it a big draw? (Did you always have dreams of trying the city for a stint to see if you could vault yourself up a few rungs of the finance ladder? Are you trying to make yourself one of the masters of the universe? Are there inimitable cultural or experiential attractions you've daydreamed about?) Is it a big turnoff? (Does the high combined tax rate rub you so strongly the wrong way that you'll make yourself miserable? Do you hate the crowdedness, the bugs and rats on the streets, the smell in the summer?)

Reflecting on questions in this vein and many more like them can help you capture how you'll feel. This helps you make a more broadly informed decision.

Job:

You've already said this is your dream job. I won't waste words here.

Relationship:

Marriage is one of the single most meaningful decisions you can make in your lifetime. It should not be approached with any set idea. There's no "eh, we've been together long enough, we should move it forward". Have you thought critically about how this person fits into your life goals, complements (makes up for by virtue of their own traits) and also accepts your weaknesses, recognizes and supports your strengths, shares similar values, has dreams that inspire you ... ?

It sounds like you're thinking about a proposal as some sort of natural evolution of the relationship that could theoretically happen now just because she's got a game face on over a potentially unhappy outcome in one other area of her life.

I say this in the kindest sense possible: that's not enough. I could go on for hours here. The takeaway is that you should explore yourself heavily, then use that knowledge you gained to examine her and how she suits you. The kind thing is to then similarly examine how you suit her (this is an unselfish, caring element many people seem to never consider). With that, you should open an honest conversation with her and spend extended time (weeks, months) exploring what your shared future could be. Propose after that, not before.

Congrats on the job at Goldman.

Getting it means you're capable and hardworking and intelligent. If you apply those to work as hard on yourself and your relationship as you do your career, you can find real beauty and fulfillment and make your life rich beyond any financial dimension.