I am so sorry for your loss! It is so difficult to lose a loved pet that you've had for so long.
We had a similar situation hit our family 2 years ago. Our pound dog of 14 years needed to be put to sleep. She had been with us since my husband and I got married and we were so crushed - she was such a big part of our life.
My son was 6 at the time and my daughter was 3. My daughter took it especially hard - my son, he was indifferent. We buried our dog in the yard, so my daughter would often visit where we buried her and cry. We didn't know what to do! We weren't expecting the reaction.
What helped her was to keep pictures of our dog on the refrigerator so she could go back and look at them whenever she wanted. We even put one in a ziploc bag so she could carry it with her everywhere. It seemed to help her to have the picture. We were determined to not get another dog for a while and this picture thing really seemed to get her through it.
We also let her know that we were sad that our dog had died. I know your daughter can't convey this in words, but it may help her to know that you are mourning your dog too. Maybe when she looks for Bubbles, you could explain that you miss her too?
In time, your child will probably focus on other things, but in the mean time, it may help to show empathy and have a few pictures around. Maybe make your child a photo album with pictures of the dog in it?
Whatever you decide, I am sure you'll do what's in your family's best interest.
One note to consider. Not only is getting a new puppy more work for you, don't forget your child's size and the fact that puppies have really sharp teeth and claws. Puppies are so gregarious, I would be afraid that a new puppy would be a little excitable and want to rough house with your child. Not only will you be potty training the dog, but you'll be performing basic first aid too! :)
Best of luck...
M.