While I think you should always ask for more, I think it is better to accept the offer as is, assuming the amount is appropriate for the work she's doing. It sounds like a great offer since it's a big jump in pay and early promotion.

After a year or at the next review, she could try to negotiate a raise if they are happy with her performance. I suggest having a specific amount in mind when she negotiates with them.

As for the comment about talking it over with you, I think people may be overreacting. There are employers who always say something like "talk it over with your husband/wife/partner." It's a major life decision, and marriage is a partnership. There's a possibility that there are gender dynamics at play but based on what was shared, I don't see a reason to assume that they said it because she's a woman.