I don't have any idea about the car.
I ... have saved around 3 times as much in the time that we have been discussing our future together despite having to pay rent and groceries (they live at home)- incomes very similar.
I guess I'm more pessimistic than most here. This jumped out at me. In the same time frame you have earned roughly the same amount but you've had to pay for the basic costs of living (rent, utilities, food) while she has had that provided for free and you have saved three time as much as she has! I'm assuming that isn't considering the car, so now their savings are less than 1/3 of yours. Unless she's been using this opportunity to very aggressively pay down student loans, I'd reconsider how 'generally good' with money your partner is. Right now essentially her entire income is 'fun money'. It isn't too hard to save money if you don't have to pay for the basics. I'd hazard a guess that a lot of folks on these forums manage to keep spending to about $100 /month/person after the basics are out of the picture.
Unless you have explicitly discussed it and made a hypothetical budget together, I'd be concerned that she doesn't have much experience budgeting and doesn't really know how car payments, mortgage, utilities, insurance, etc. will add up. Suddenly her available 'fun money' category is going to be a LOT smaller than what she is used to.
I'd also be wary of buying a house together. I'd suggest either renting together for a while, or you buy the house and she rents from you. Perhaps with some agreement stating that after you are married/civil partnershiped/ been living together more than X number of years she gets a percentage of equity in the house related to the rent she's been paying.
If you still want to buy a house together it's probably a good idea for you to sit down next to each other and write out individual detailed budgets so you both know what the situation would look like. "Honey, I can't make my half of the mortgage this month, you don't mind covering it for me do you?" Is not a situation you want to wind up in. And draw up an agreement on how ownership of the house would work. My roommate and I have been considering buying a house together if the right one comes on the market and we have been making a list of 'what ifs' that we will put into a contract if we end up buying a house (what if: one of us dies, one wants to move in a SO, one wants to move out, one wants to sell one doesn't, one want's to lease their part of the house, one of us does more labor fixing it up, we disagree on rehab/repairs, major work needs to be done and only one of us can afford to pay for it, one of us loses a job, etc.)
Disclaimer: I'm probably extra grumpy about money and relationships. I just got out of a relationship where money was one of our issues and I also felt a lot of confusion about whether my concern was justified or if I was being controlling. Financial concerns didn't become an issue until we seriously started thinking about combining our lives, but (fortunately) everything went south before we moved in together. Because of our disagreements about money, I found MMM, so something good came out of all of it.