Kris,
If you are a new rider I wouldn't recommend the power of a Ducati as a first bike since there is a lot of variables when learning.
However, if you're just starting out with a bike and you want a Ducati I would say a smaller monster would be a good as "forgiving" as a Ducati you can get since the 620 monster would be not tons of horsepower and still plenty of torque and a well handling bike.
Learning on a bigger Ducati would be far too dangerous for a first bike. I don't say that because you're a girl, but just in general as a new rider you want to learn on something that is easy to learn on and learn the dynamics of throttle control and learning braking. It is very easy to get yourself into trouble (even if you are careful and self preserving) on a large bike.
I ride a Ducati 900SS, I enjoy the desmodue engines from Ducati because the powerband is usable throughout the whole powerband and gears on the street (unlike a superbike like a 999 or a 1098 which is overkill for the street and you'll never use the whole bike) and it is also EASIER to maintain and you can do the maintenance yourself if you are a do it yourself type.
I still say go with a monster 620. For one, you hardly see them around anymore, they still have great power and you are small so they are easy bikes to fit on and ride around. They are very maneuverable, you will find them a great joy in the corners and they have an aftermarket that is out of this world.
If you are open to other brands, other really good beginner bikes would be a Bandit, SV650 (since they are far more smooth than an inline 4 and forgivable power band), Ninja 250R (EXCELLENT beginner bikes to learn throttle control and braking).
Best of luck to you. Be safe. Remember to ride within your limits and live to ride another day

There are old riders and stupid riders. There are no old stupid riders.