Never do spiritual cleansing with animals nearby, especially if deep.
They absorb negative energy and spiritual dirt!
They are highly sensitive; I realized this by meditating near my cat.
In any case, if you do color meditations or sunlight meditation, or vibrate mantras or runes for positive purposes, there is no problem.
The important thing is that you don't implement black magic spells or do spiritual cleansing when you are near your dog, because it could be really detrimental to him.
It would also be ideal, since you value your pet's company when you meditate, to do a gentle cleansing of his soul a couple of times a day.