Charlotte hi - just to let you know, I appreciate that the title alone of the website doesn't distinguish between professional and family carers, but in fact this forum is for family carers! So isn't really targeted at professional carers such as yourself.
However, in respect of taking your dog in, I guess first and foremost it must be at the discretion/permission of the care home, so I would raise the issue with your immediate suprerior, or ask the manager what the policy is (You might like to ask the resident cat but I expect it will have strong view of its own ho ho ho!) (my cat certainly would!
There may well be health and safety issues etc, but on the other hand, maybe even if you aren't allowed to bring your dog in every day (after all, where would it be while you were working, eg, helping to hoist a patient, or at mealtimes etc etc etc), you might be allowed to bring it in say one afternoon a week??
I definitely agree that many patients would love to see a dog and gain great cheer from it - I know at my MIL's first care home relatives would sometimes bring their dogs in (by agreement with the home's manager) and many of the residents liked to pet and stroke it. Also her current home has two resident cats who make themselves very much at home in the rooms, in the lounges and so on, and are favourites with many residents.
That said, of course some residents may NOT like animals at all - and some may also be allergic??
Hoping you get a positive answer from you manager - all the best to you.