Hi A.,
Great question! My daughter has some food allergies, so I've had to be creative about snacks...the traditional crackers just don't cut it for us. I have a couple of suggestions for you, depending on how your 1 year old is with chewing.
A friend turned us on to fruit leathers. Costco carries some all-natural (just fruit pureed and cooked until gummy) ones for a reasonable price. I have a few recipes to make them, but haven't tried them yet. You'll probably have to cut them into small bits for your little one. They travel well as they're sealed in individual packages and don't crumble, but they are sticky.
Any dried fruit would travel well and help with constipation. There are also freeze-dried options available, which I personally prefer for texture. I think Trader Joe's and Whole Foods carry them in larger containers. In the regular groceries, Gerber has packages tiny toddler-sized bits (strawberry and banana, I think).
We like cheese sticks, but they tend to contribute to constipation.
We found a product at Whole Foods called "Red Square Flaxmachine Flax Cookies." They are made of rye flour and ground flax seeds...They are FANTASTIC when constipation is an issue. They're expensive, but a little goes a long way. They are very crumbly, so they may not be the best for travel, but I'd definitely recommend them for home. They taste great with banana, too. There's a picture of the label here http://www.rsquare.com/flax.html. What we buy is second from the bottom on the right-hand side.
If you're past the choking-hazard point with your little one, almonds would also be a good snack. We're just starting them with my 2 year old, because she's been a slow teether, but she really likes them.
If you're starting citrus fruits, the little clementine oranges are great for going out. They peel and pull into segments easily and aren't too terribly messy.
A friend buys all-natural yogurt tubes at Costco. She says they don't have the artificial colorings and flavorings of the Go-Gurt at the regular grocery store. Her son loves them.
If you're not too bothered by a little mess, my daughter loves large curd cottage cheese, and it doesn't seem to constipate her as easily as cheese.
Good luck!