Upon passing on from Malcolm of the IoW order.

I can finally face doing this for Brodie 

 Eternal Lord and Lady who are there with love for the smallest sparrow when it falls, who know the wonder of joy and the agony of despair and who delight in all that they have made, we give our loved one ............... into your care.

..............., we remember you.
At the rising of the sun and at its going down, we remember you.
At the blowing of the wind and the chill of winter, we remember you.
At the opening of the buds and in the rebirth of spring, we remember you.
At the blueness of the skies and in the warmth of summer, we remember you.
At the rustling of the leaves and in the beauty of autumn, we remember you.
At the beginning of the year and when it ends, we remember you.
As long as we live, you too will live; for you are now a part of us, as we remember you.

..............., you came and touched so many hearts in so many different ways. You gave so much and asked so little in return. We know you are safe now and nothing can harm you. Remember, although you are apart from those who love you, you will always be together.

Deep peace of the running waves to you
Deep peace of the flowing air to you
Deep peace of the quiet earth to you
Deep peace of the shades of night to you
Moon and stars, always giving light to you.
Blessed be.

..............., rest from your travels in this existence and when you are well rested and ready for your new adventure to begin, may you hear our words on fresh breezes, an ancient blessing on your new journey.

May a new road rise to meet your feet,
May a gentle wind be always at your back,
May the Sun shine warm upon your face,
May the rain fall softly upon new fields,
Until we meet again
May Spirit guide you safely to a new land.
So may it be.

..............., may your journey be Blessed.

For the ritual, perhaps choose a place which your dog enjoyed. 

Set up a small altar with a few mementos of your dog. It's collar, favourite toys etc. 

Light a candle at the start and extinguish it at the end. Add to the ritual a short period of meditation to remember all the joys of the dog's company. 

Leave some water and a few animal and bird-friendly treats so tha other local denizens can celebrate your dog's life.