Will she take fluids better from a bottle? If so, you might consider giving her more water or juice/water mix from the bottle for now--perhaps she's not ready to drink mostly from a sippy cup. My daughter didn't like the sippy cup much at that age, so I found one with a silicone top (Munchkin brand at Target) that felt more like a bottle, and she drank water and juice eagerly from it. I used white grape juice, as apple juice can be constipating and wg juice is not. At times I also gave her prune juice from a dropper (she wouldn't drink it from a bottle or cup, but she likes medicine so I made it her "poop medicine" and she drank it up--usually 1-2 tsp/day). Also, if she likes finger foods, try cutting up a prune and feeding her one or two prunes each day. My daughter ate them eagerly (to my surprise) which helped get her through several constipation spells. If that doesn't work, try giving her more fresh apricots and plums, both of which help with constipation, and lessen her intake of constipating foods. In general, darker-fleshed fruits help with constipation, while lighter fruits can worsen it (like bananas).
Another thought, when my daughter switched to toddler formula, it really constipated her. If yours is on a toddler formula, try mixing it with baby formula or switch back to baby formula until she's 1. Good luck!