Hi! I've taught preschool and kindergarten and the following books have been some favorites although they aren't about puppies or dinosaurs. Hope this helps.
Chicka Chicka Boom Boom by Bill Martin Jr. and John Archmbault (I'm not sure on the spelling of his last name)
Chicka Chicha 123 by Bill Martin Jr., Michael Sampson and Lois Ehlert
Brown Bear, Brown Bear by Bill Martin Jr., pictures by Eric Carle
Polar Bear, Polar Bear by Bill Martin Jr., pictures by Eric Carle
The Very Busy Spider by Eric Carle
The Very Hungry Caterpillar by Eric Carle
The Very Quiet Cricket by Eric Carle
and other Eric Carle books
Caps for Sale by: Esphyr Slobodkina
Is Your Mama A Llama? by Steven Kellogg
The Napping House by Audrey & Don Wood
Quick as a Cricket by Audrey & Don Wood
The Little Mouse, The Red Ripe Strawberry, and The Big Hungry Bear (all one title) by Don and Audrey Wood
There Was an Old Lady Who Swallowed a Fly by Mary Ann Hoberman and Nadine Bernard Westcott
Peanut Butter and Jelly: A Play Rhyme by Nadine Bernard Westcott
If You Give a Mouse a Cookie by Laura Numeroff and illustrated by Felicia Bond
If You Give a Pig a Pancake by Laura Numeroff and illustrated by Felicia Bond by Laura Numeroff and illustrated by Felicia Bond
and other "mouse" books in this series
Five Little Monkeys Jumping on the Bed (and other 5 Little Monkeys books)
Stellaluna by Janell Cannon
Verdi by Janell Cannon
We're Going on a Bear Hunt by Michael Rosen