Hi,
i was browsing through and found your question...
I've ridden road bikes for probably 30 years and still wouldn't know what to choose in a short amount of time.
I wouldn't jump into buying anything so fast..or if you are super keen to get riding and stop borrowing, get a second hand bike and ride for now but keep looking for a while.
For one, you don't need a fully carbon fibre bike..that's SUPER high end and many pro racers don't even have that. I ride an Olmo (italian frame) Aluminum with Carbon stays and forks. it's a stiff ride (good if you ever want to race or you like to ride FAST into corners, etc. but the carbon fibre dampens the ride a lot).
You can get frames and get your bike built up with whatever you want or you can get a kit bike like the Trek you described and others. Terry Bikes makes women's bikes also (type Terry bikes into Google), it's woman run co.
Components are a question too. you can go with the popular Shimano but serious cyclists will tell you that Campagnolo is better (ex. if you bend your derrailleur like I did, in the Shimano you have to replace the whole thing - expensive! - but I only had to replace the hanger - cheap!)...
Try a few bikes before you buy. You want a frame that fits your body type and your "riding style/objectives". All frames have varied geometry that are designed for specific styles of riding - figure that out first before you buy. The Components you can always upgrade later. Go with what works at first, maybe a cheaper wheel set, etc. at first and upgrade to higher end Carbon fibre components later on.
Once you ahve your perfect frame, the rest is fun to upgrade as time goes on. This year i am buying new carbon fibre ergonimic handlebars and a new wheel set to upgrade (haven't upgraded anything in 6 years)...I'm excited but it'll run me about 2,000 bucks! It'll FEEL like a new bike though! :-)

Anyway, i hope you get my drift. Bikes can be a BIG purchase and can be expensive but think of it this way;
In your car, you can adjust your seat, drink your coffee, use a lumbar pillow, etc. to make it more comfortable....on your bike you don't have those options. If you plan to ride a lot...you want a frame that fits and then you want good components and accessories, you don't always get all that in one package, sometimes you need to go looking for it. After 100km on the road on Sunday morning, you'll be happy you took the time to do that, trust me on that one!

Good luck!
welcome to the world of roadies. I LOVE it, there's nothing else like it.