This is Bunny and Frog. It is the first book in a series by US author, William Leaird Meadows.
Bunny and Frog, are best friends with Turtle. They discover it’s Turtle’s birthday and go out to find the best present for him.
They treat it like a competition and put their friendship at risk over their eagerness to please Turtle when all he wants is for them to be there for him and sing him songs.
The story’s message is that material things don’t matter when the joys that friendship brings is all you need.