We have that sippy cup too. I agree with Kage, 3 months might be a little young still. Our TT sippy has quite a fast flow quite a fast flow and it takes more skill and coordination to drink from one than it does to drink from a bottle. I think it's likely it would just frustrate her at this stage, plus you want to make sure most of it goes into her tummy and with a sippy cup it could easily end up everywhere BUT in her tummy!
My LO is 8 months old and only recently mastered the sippy cup. There's no way he could have drunk his milk from it even at 6 months.