My 11 week female Australian Shepherd Mix is timid of dogs barking in the neighborhood, loud noises etc. but is not the least bit afraid of our 4 year old, 100 pound Lab mix.
Today I picked the plastic grill cover off the ground as my puppy was standing by it and she ran to the door. As soon as I opened it she ran to her crate and has been whiny and clingy for an hour or more.
Hi Kathy Puppies are just like children, they're all different with different temperaments and personalities.
It sounds as though your pup is naturally on the timid side and a bit anxious, but the facts that she isn't afraid of your bigger dog, and that you don't mention any fear-aggressive tendencies are good signs. She is likely just a bit 'shy' and nervous and that's not something you'll just need to work with.
For pups like this, early and continued socialization is very important. These experiences should always be positive and you may need to move a bit more slowly than with a more confident pup. I'd recommend that you read my Socialize Your Puppy and the other related articles to learn more about how to do this properly.
Collies are very intelligent dogs and they thrive when they have a 'job' to do, that also helps offset their sometimes high-energy and anxious personalities. I'd suggest that as soon as she's fully vaccinated you enroll her in a Puppy or Basic Obedience class at a local dog obedience school. This is also a great socialization experience for puppies.
Make sure that you don't 'baby' or coddle her when she gets scared as that tends to reinforce in a dogs mind that there REALLY is something to be scared of. Always use an upbeat, confident tone of voice and approach her training and socialization with a happy attitude. She will pick up on that. Dogs take their 'cues' from their owners and she will pick up on your attitude, so make it a happy, confident one.
Always give her lots of praise and treats when she's successful at something, and never scold her harshly or raise your voice. With lots of love, patience and consistency she will outgrow this timid behavior as she matures and gains in confidence.