"We have a little black dog."
It can only be omitted in some cases. Most importantly:
- For possessives: 的 is optional if the possessor is a personal pronoun and the possessee is either a person with close personal relationship to the personal pronoun (e.g. 我(的)妈妈) or an institution that the personal pronoun is part of (e.g. 我们(的)公司)
- for adjective attributes: 的 is optional if the adjective is only one syllable and not modified by any adverbs (so 黑(的)狗 or 黑狗, but not *黑色狗). Also, if there are two one-syllable adjectives, I would use 的 at least on the one that is further away from the noun (in other words, I think 黑小狗 sounds a bit odd; I prefer 黑(色)的小狗).
The accepted answer here is useful https://chinese.stackexchange.com/questions/9190/what-are-the-rules-in-chinese-for-adjective-order-when-multiple-adjectives-descr
I don't have a chinese keyboard installed on this device so I'm afraid it's pinyin only. Adjectives with 'de' must be further away than those without. So 'heisede' must come before 'xiaogou'. (And as a single syllable adjective 'xiao' does not need 'de'.)