A two-year old is much too young for either ballet or gymnastics. I have three children who have been professional dancers, and no decent dance school starts a child on formal ballet before the age of six -- maybe even older for some children. Before that, you need a creative movement class, and a two-year old is even too young for that. Put on some music and sway and clap to the music with your daughter. Make rhythm instruments of pots and pans (or you can purchase a simple set) and use those to have fun moving to music. Try skipping, jumping, hopping. I've been around gymnastics training, and I think you'd get a similar answer from anyone in that field.
Around four years old, you might find a very good class in creative movement for children, and spend two years there. Also, Yamaha has excellent classes that are theoretically piano classes for quite young children, but they also include rhythm and are good training for eye-hand and any kind of movement. Then it may be time for ballet or gymnastics.
Don't burn your child out, or turn her into one of those children who "does" ballet for 6 months, and then goes on to the next thing. Your child may never decide to be a dancer or gymnast, but good training in dance, music, or movement at the correct age by excellent teachers will be of life-long value and enjoyment.
S. Toji