My dad has just started chemo for SSC, primary in the nasopharynx, spread to lymph, spine and hip mets, he is having cisplatin & gemcitabine 1st week, carboplatin 2nd week, then 1 week break, for 6 rounds. He completed his 1st round just before Christmas.
My dad wasn't able to go alone, he cannot drive at the moment, but that's due to his cancer being very symptomatic, if you are well in yourself I can't see why you couldn't go by taxi but would advise against the bus, you'll likely be quite tired after treatment.
He took a packed lunch on the first day, but they came round with lunch options for everyone so he didn't need it, I recommend taking boiled sweets as apparently you can get a nasty taste in your mouth.
Each bag took 2.5 hours, so week 1 he was there for 7 hours, 2nd week less than 3 hours.
My dad has a cat, no one mentioned pets to him. The nurses on my dads chemo ward are really lovely, as I'm sure yours will be and they'll be happy to answer any questions you have.
I wish you all the very best with your treatment.