Actually that is kind of scary, most companies supply you with a work device so it can be securely administered. That's kind of a red flag that they accept you working from whatever you have.
Get the laptop if you can, you can probably claim it for a reduction of taxes (keep the receipts). Keep it separate, always. You'll appreciate being able to close the "work device" when the day is done. Also, very much lock it down--do not let friends/family "borrow" your laptop.
People do the worst crap on computers that aren't their own.