Potty training ?

Natalie has taken an interest in potty training.  She's all about sitting on the potty, reading her potty books and playing with her potty wand.  She's peed on the potty a few times but every time she does, she gets startled, stops the flow, and jumps up to check the potty, and wants to dump in in the toilet and wash her hands right away.  But I know she's not done because she'll only go a little before jumping up.  She'll sit back down and not go again.  She of course then fills her diaper once it's back on.  All this I expect is pretty normal and just her needing to get more used to it but I've also noticed she's starting to hold it and not go in her diaper either.  Today for instance, she was dry from about 9 a.m. till 1 p.m. when she finally went in her diaper during her nap -- she wouldn't go on the potty either.  The last few days she's starting holding it for long periods of time -- it's great that she's learning to hold it but it seems too long I think.  Is this normal when they're learning how to use the potty -- not wanting to have a wet diaper but not using the potty?  I don't want her to get an infection.  Is there anything I can do to encourage her to let the pee come out when she's on the potty?

I should add she's also waking up in the morning with a dry diaper but not letting it come out in the potty.  Waiting for a half an hour or so before going in her diaper.