All sound idiomatic.
There is a very slight difference in meaning between the first and third and the second.
The first and third statements (interrupting and disrupting respectively) say explicitly that the dog has been waking you: you were not always asleep; your sleep was broken.
The second statement (disturbing my sleep) says explicitly only that your sleep was not normal without necessarily saying that you were awakened. The second statement does not formally deny that you were awakened; you may have been. The second statement simply does not positively affirm that you were awakened.
If you want to imply that you were awakened, then I would use the first or third versions. You may want to note that "interrupt" is a more common word than "disrupt." From Google Books.
If you want to leave it ambiguous as to whether you were awakened, I'd use the second version.
But I must admit that at least 99 readers out of 100 will view all three as saying that you were awakened and are saying it idiomatically.
EDIT The following Google Books graph
provides strong evidence of my initial point that all three phrases are idiomatic although Ngrams looks only to published writings and may not reflect relative frequencies in everyday speech. However, my personal experience is that in this case relative frequencies in speech are at least roughly similar to those in published writing. I am grateful to user070221 for providing the ngram citation.
What ngrams cannot do is to address my second point, namely that the three statements may not be interpreted as having perfectly identical fields of meaning.
I think it interesting that the slightly more general phrase is used by published writers more frequently than the slightly more specific ones