The two of you can have a future if it is based on love and not what society or others think about the relationship. You and her will have to really figure out what the "future" will look like (you've already decided not to have children) As long as you have things in common and care about one another, then yes, you can have a good relationship. Love should not be blind. As far as wasting your time (it would depend on what you want out of the relationship and what compromises or sacrifices the two of you are willing to make) It may be wiser to give it another year and see how things develop. Couple's of different age do not really handle it any more differently than others (there are many scenarios where the male is older) How things are handled is what the two partners decide to work on and make it happen.
It has to go both ways (if she can not be flexible) then you making a sacrifice won't work. The cats do not and should not take a place of a male companion/lover/partner.
You may just want to see if she changes with time (you decide how long you want to give her) You can only live in the present moment. Projecting yourself into the future is not helpful nor it offers any guarantees of how the future would turn out to be.
She may be trying to figure out things herself (she should not also say she can't live with someone- it has to do with what she wants to do versus can't) Because technically she is capable of living with someone (you) The question is does she want to?
Unless you are allergic to cats, there ought not to be a problem. Cats are pets and a you are her partner.