Loving this poem, I like how it begins with the thought of getting up so early, and I can feel the tiredness and unwillingness to get out of the bed to let the puppy out.

you then take us down to the kitchen where we can begin to see the normal routine that surrounds this little puppy, and how she has the owners trained ;p

mother natures lullabye = nature's

As for titles, there is many you could take. If you want it based on nature side of the poem, I suggest peace and calm that Spring brings, you could have Spring Morning's. Or Morning Glory, or Priceless Moments,

The poem itself is quite centred around the dog, so perhaps you could add that tot he title? Dog Duties , Puppy Patrol.

Hope you find a title soon. Write more soon please xx

Routine would be a good title....is all I can come up with right now.