At only nine weeks, she is very much a baby. you need to take her out as soon as she wakes up from a nap, after she eats, after she has a good long slurp of water, after she's been playing for a bit, any time she looks like she's thinking about pottying (sniffing, circling, etc.) and ever twenty minutes or so just because. She's still peeing in the house because you are missing her signals that she needs to go and/or expecting her to hold it too long.
You train her to go to the door by taking her there, asking if she needs to potty, and then taking her out. Eventually, the act of going to the door will be associated with the act of going out to potty. And be aware that she might not use "going and sitting at the door" as a signal she needs to go out. Neither one of my girls does that, but instead tend to stare at me, nose poke me, and/or whine at me