Driving in the Dolomites as a solo woman is totally doable and generally safe. The roads are well maintained and italian drivers in the north are way more predictable than in the south lol.
Your itinerary looks pretty solid! Just a few things to keep in mind:
The mountain roads have lots of switchbacks/hairpin turns. Take em slow, especially if you're not used to mountain driving
Parking in Cortina can be tricky in peak seasons. Most hotels have spots but double check with yours
For the Lake Braies drive, try to go early! The parking lots fill up crazy fast and you might have to park pretty far if you arrive after 9am
The drive to Milan will take around 5-6 hrs depending on traffic. Plan for breaks since mountain driving can be tiring
For the hiking day - definitely recommend going with a guide first time. They know all the best spots and weather patterns, plus its nice having someone who knows the area when hiking solo.
Quick tip - if youre not super confident with Italian roads/signs, might wanna check out Tripiamo before your trip. They've got really helpful guides for driving in Italy that cover everything from road rules to common situations youll run into in the mountains.