Even a 2 year old is capable of learning about budgeting. While she probably doesn't really comprehend "saving" yet, it is something you can work on simply by giving her some money, and talking about choices. Talking about the difference between buying a small, cheap toy now, versus saving some money until she can afford a larger, more interesting toy, helps, even if it doesn't immediately lead to her choosing to save; over time, she'll understand, particularly when she gets frustrated that she doesn't have the money for the larger toy.
Setting an allowance - i.e., a certain amount per week set aside to buy things for her that she wants - is one good way to do this. Even if you're not handing her the money yet (since she's too young to actually have coins yet), you can still define this allowance - effectively, the "buy things for your child" budget. That amount should grow over time - both because older children want more expensive things, and because it's good to give them control over more of their expenses (thus, allowing them to choose to spend more in one area than another - one core concept of budgeting).
If you only have one child (and only intend to have one child), then you can set the budget to whatever you consider reasonable. Perhaps start with what you would normally spend buying her toys/etc. that she didn't ask for; take that annual amount, divide by 52. Discuss it with her, and let her know when she has an opportunity to spend some of it. At 2, you're going to control those opportunities; as she gets older, she'll have more opportunities to define when and where she spends her money.
If you have more than one child, as I do, you have to decide how to equitably set allowances at different ages. My parents tended to give us all the same allowance, regardless of age difference - it was based on their ability to give us money. That felt unfair, as the eldest. For our children, we give an age-based allowance; some fixed amount times their age, so (for example) a 4 year old gets $4, a 8 year old gets $8, etc., adjusted for ability to pay and parental preferences (so maybe you prefer $.50*age per week, or $2*age per week, etc.)