Do I love her the right way? I deeply care about her. I'm not sure I can identify what it means to marry for the right reasons.

I can tell you what some of the wrong reasons are.

a) Sunk cost fallacy. She doesn't want to break up because you've both invested so much time/effort/money into the relationship.

b) She wants to have babies, irrespective of what you want.

c) If you have a baby, maybe that will bring you guys closer! (:facepalm:)

Caring deeply for someone is love, but it sounds like you want more than that. You want someone you care for and that you feel passionate about. Do you feel passionate about this woman? Do you get home, and when you see her, oh my lord she's the one, I want to fuck her brains out, marry her, hug her, kiss her, make love to her, all in one? Does she, my friend, make you lose your shit, in a good way, on a regular basis? Is THAT what you're looking for? If it is, and she's not doing that for you, you're gonna have a bad time.

Especially if you marry her and have a baby.

Know this from experience.