Being told to travel with less than a day notice

I’m new to consulting but have generally enjoyed it over the last 4 months, aside from some minor things. I have a dog I have to board, but because I can take per Diem most jobs, it’s not too bad. I was told when I was hired I would generally have a week or 2 notice for jobs and my supervisor knows I have my dog and is typically understanding. However, my supervisor called me today and said they may have a job next week I would be needed for. No big deal, I can usually get my dog boarded on a day or 2 notice. He then told me I may not know till the morning I needed to travel.

I understand I started working for a consulting company, but same day notice is a little tight. I told him I’d still be willing so long as I could get my dog to be boarded the day of, but if not I physically can’t just leave him in my apartment for 2 days. The response was “I get that, but it’s not really a request. It’s an important job so if we tell you to go, you’ll have to.” Again, last minute jobs happen and I’m always willing. I’m new to consulting, but that can’t be an appropriate response right? I would have to reschedule a doctor appointment next week for the job, which I’ve already had to reschedule because of 2 other short notice jobs. I don’t mind doing rescheduling, but doing it every time I book a new appointment is getting old. Plus it’s a toss up if the rental car companies would have vehicles the day of. I was fairly content before but this response is pretty unusual, so I’m wondering now that I’ve been there a few months that’s how the company actually is.