Kuddos for wanting to go to a straw ASAP. Sippy cups maintain a suckle while straws help develop a true suck. And drinking from a cup without a lid is even better! Sippy cups are great for floors/rugs but not so good for mouths. (I'm a pediatric speech-language pathologist who ISN'T looking for more kids who need help developing good jaw, facial, and tongue muscle tone!)
You can try a juice box that you hold & squeeze gently to get the liquid to the top of the straw, then release when your daughter tastes the juice. For some kids, that's all it takes.
There are other tools I use that I get from the feeding tools section of Talk Tools: http://www.talktools.net/ No, I don't get a kick back :) You can use the honey bear with a food grade flexible tubing straw the same way you use the juice box. The advantage is that you can see the juice level in the straw in the bear, easier than in the juice box. You can either buy the bear with the tubing, or just buy a length of tubing for less than a dollar & buy a honey bear at the grocery, eat the honey & save the bear as a straw cup. I have also used the Infa Trainer cup for children as young as 8 or 9 months, and the recessed lid cups for training both cup drinking and straw drinking.
It's worth the effort to help your little one move forward with her oral motor development. Good luck!