Toilet training - carpeting a previously hard floor

[3AndADog]

Hi,
We have a wooden floor in our kitchen/lounge, we removed the huge rug on day 3 with pup when she weed on it and we decided it was easier to remove. She’s 8 months now and we recently put a door mat in the lounge by the back door and she weed on it immediately, having previously always pawed at the door when she wanted to go out. I really want to get a new rug for the room as I really miss having a cosy floor but how can I put her off using it as a toilet? Is there something I can spray on it to make her Not want to wee on it?

I'd be tempted to...

a) first put a rug down away from the back door - so it's geographically sperated from the place she goes before going to the toilet (i.e. she has to go to the door before going outside)

b) be quick on the draw to make sure she gets put outsie when going near the door; no loitering with intent

c) do something else with her on the rug so she has lots of chance to stand on it without peeing - training tricks, for example

d) assuming she doesn't pee on the rug when it's at the 'wrong' side of the room, slowly move it across to where you want it

I was terrified that our pup would pee on our expensive new rug. Google suggested spraying it with a dilute vinegar solution so I did that. He never peed on the rug but it could have been coincidence

We got him at 6mo (rescue) and he was already toilet trained and has almost never peed in the house but we do have hard floors downstairs. The time DH put a dust sheet down to paint was the only time he ever peed in the house. As soon as it went down he peed on it and when DH got a new one he did it again! That's what made me worry about the rug
So either the vinegar worked or rugs are different to dust sheets in his mind.