We had our beagle Cookie, and thought it would be good to help home a dog from one of the countries (Cyprus, in this case) that tend to not treat them well in general. It was really exciting to think that Cookie would have a new mate in the house.
So, the arrangements were made. We had to wait a few months till Pickle was old enough to handle the trip from Cyprus to England.
A week before Pickle was due to arrive, we lost Cookie.
That was so hard. The grief was immense. But a week later we had a new arrival (that needed a lot of care, love, and attention - Pickle was scared of her own shadow). Sure, there were times in those early months when it kind of felt disloyal. But we had to push any of those thoughts away and focus on the fact we were giving another dog a chance at having a contented life. And there's no option, once they're with you they rely on you.
Would we have chosen that path if we'd known Cookie wasn't going to make it? Possibly not, I have to say. Well, not that fast anyway. But it did teach me that would probably have been the wrong way to think about it. Cookie just wasn't here any more, and there's nothing that could have been done about that. We had that chance kind of thrust upon us to give another dog a chance, and that was the right thing to do.
And what we found, of course (and as we all know), is that it doesn't take long to reach the point where a dog or cat (I don't know anything else, so can't say) has become an intrinsic part of life where you can't imagine being without them.
You clearly have a lot to give a new arrival, Alan. Feelings of disloyalty certainly shouldn't be a part of that, although they will likely surface at times. Based on personal experience, I'd say go for it. With the knowledge you are not 'replacing' Tilly, as Tilly did not 'replace' Lucy or Rabbit Catcher. If anything, the new arrival will honour those that came before.