We first took my son to DL when he was 11 months. He was not walking yet, so he it was easy for him to be in the stroller. I distinctly remember him liking Dumbo and It's A Small World. He wasn't talking yet, so he clapped when Dumbo started moving...I took that as a positive sign!!
Honestly, I think you could take your 1 year old on most things. But it depends on her...will she sit in a ride for 5 minutes and not try to climb out? Is she afraid of the dark or loud noises? Start with the easy rides...Dumbo and Aladdin, if she likes them, move on to It's A Small World. If she likes that, try Peter Pan, etc. Probably the only ones I wouldn't try with her are: anything that has height requirement (duh!), Snow White (my son still won't go on that and he's 4), The Haunted Mansion (my son goes on that now, but not when he was 1), Pirates (again, he goes on it now, but not when he was 1...although since the WDW version is shorter than DL, she might be able to sit through it), Mickey's PhilarMagic (too intense for a 1 year old, I think).
Have fun! My son, at 4 years old, is now a DL veteran! We have our first WDW trip next month.