I wouldn't rule out doing a CT scan for my pet, but it would depend on the problem and other things like age and general state of health, etc.
One of my dogs died of a brain tumor two years ago. Symptoms came on suddenly and left no doubt what the problem was (she was falling to the right, and her eyes were shifted off to the side). It was clear we had no choice but to end her suffering.
What makes your vet think there's a tumor? What will you do if a tumor is found? What will you do if there's no tumor found? How will you proceed if you don't do the CT? Will you go into debt to pay for it, or can you comfortably handle the payment? These would be questions I'd be asking myself if it were my pet.
Not doing a CT doesn't mean you don't love her. It may or may not be the right thing, it just really depends on the circumstances and what you'll do with the information. Someone who chooses not to do a CT would probably take a "wait and see" approach. If it is in fact a brain tumor, you'll have your answer in time. In the meantime, love her like crazy, and promise her you'll see it through to the end.
Good luck. It's never easy when our beloved pets become sick.
P.S. I'm not positive, but I don't think chemo (or, I should say, chemo
alone), is very effective on brain tumors (because it doesn't cross the blood brain barrier). In people, they generally use surgery and sophisticated radiation to treat brain tumors. I don't know if that's something that would normally be done in a pet; and if it was, I can't imagine what the cost would be (not to mention, suffering of the pet). I can do a search and re-post here later.