If you were my client, I would tell her "thank you, I appreciate the offer. Please come back once you have a pre-approval letter from a lender and we can proceed at that point." Until anyone demonstrates they have the capacity to qualify for a mortgage, equal to or greater than is necessary to purchase your home, you are on the market ready for a buyer. Don't sign anything with her, or anyone else without proof that they are qualified. In truth, if I were your agent I'd take several steps beyond that including calling the loan officer involved to find out whatever details they would disclose to me.
Is it possible she could get financed, yes. Is it likely, debateable without a lot more information. Don't take her word for it, get the pre-approval from a reliable local lender at the minimum.
Best of luck, let us know how things turnout.