now I've got the idea the bag she paid for was much more expensive than the one I think is the same bag.I agree you are making this much too complicated and perhaps assuming too much.
Every designer bag has its designer label/attachment on it, all you do is look up the designer and match the bag, they all look different not hard to match it. If you have matched the same design to the make you've got the bag end of.
However, I would also err on the side of caution, there are many, many, many fake designer bags around, they are everywhere, only on close inspection can they often be spotted. This could well be a bag under £40.
I would not be putting my £400 designer bag on the floor or take it into work where I worked with dogs, but I guess not everyone is me.

I would also price check Debenhams, John Lewis, House of Frazer for price checks too, very often there are
sales on, so don't miss out, she won't worry what you pay for the bag just that it is the same.
In future when you take the puppy, I would call out to the whole office that the pup is here so could everyone pick up their valuables.
Stop worrying, it is up to her to tell you the bag is wrong, or more expensive, if she says nothing, then not much you can do, just buy the bag and hold your head up, you've done the right thing.