Is this Fireplace Safe?

To answer your question, I decided to experiment with your build. I tried to replicate your fireplace as accurately as I could, while limiting the size of the structure surrounding it:

I tried to keep the base structure of the fireplace as close to identical as I could.

I first attempted the fire with the wood planks shown in your pictures:

Unfortunately, the wood burned down to nothing, and the fire eventually died. I then tried it with Netherrack.

Everything seemed to be going well. I thought I'd successfully completed the experiment, when suddenly:

EVERYTHING QUICKLY WENT HORRIBLY WRONG!!

The end result to follow:

Alas, my structure (house) was destroyed. I feel I didn't even get to know my creation, for it died within minutes of me setting the fire.

Long story short, NO. The fire will spread to your house.

five wooden blocks were harmed in the making of this answer

EDIT It is worth noting, however, that out of the 4 times I've rebuilt/retested, every time the fire has started at the bushes along the outside of the fireplace.

I would say no From the Wiki

More precisely, a fire block can turn any air block into fire that is adjacent to a flammable block and up to one block downwards, one block sideways (including diagonals), and four blocks upwards.

Also, this answer would suggest not as well.