A slightly different approach that I've just tried (successfully) on the first few bars, but it will take time - pick out sounds from elsewhere in the sound file that roughly match the sounds the dog barks over, and copy-paste them over. You may not get rid of every single bark, but most of them. Fortunately the guitar accompaniment is... erm... uncomplicated!

Okay, I'm quite used to doing such edits, and find it relatively easy to do - but it is painstaking and slow. I use SoundForge, but for this kind of thing Audacity will do almost as well.

The advantage is that you're not trying to filter out the noise, but replace it, so the results should be seamless.

The audio is mono (as Treewind suspected), and not that good to start with... it's nearer to telephone quality, really - 22050Hz, 16 bit.

Be careful when copying and pasting that you try to set the markers in 'null points' - where the sound wave crosses the 'centre line'. That will avoid nasty clicks.