An important thing to mention regarding kamma and rebirth is that there are also past kamma that has not yet ripened and come to fruition. If the right conditions are present past kamma can come to fruition thereby resulting in a higher rebirth, e.g. as a human being.
It is like a seed. If one nurtures the seed with water, nutritious soil, sunlight and other conditions the seed might blossom and turn into a flower.
Kamma is fourfold and is divided into sections, i.e. "by way of function, order of ripening, time of ripening and place of ripening".
Kamma by time of ripening is further subdivided into 4 types according to the time of taking effect:
(i) Immediately effective (diμμhadhammavedan2ya) kamma is kamma which, if it is to ripen, must yield its results in the same existence in which it is performed; otherwise, if it does not meet the opportunity to ripen in the same existence, it becomes defunct. According to the Abhidhamma, of the seven javanas in a javana process, the first javana moment, being the weakest of all, generates immediately effective kamma.
(ii) Subsequently effective (upapajjavedan2ya) kamma is kamma which, if it is to ripen, must yield its results in the existence immediately fol- lowing that in which it is performed; otherwise it becomes defunct. This type of kamma is generated by the last javana moment in a javana proc- ess, which is the second weakest in the series.
(iii) Indefinitely effective (apar±pariyavedan2ya) kamma is kamma which can ripen at any time from the second future existence onwards, whenever it gains an opportunity to produce results. This kamma, gen- erated by the five intermediate javana moments of a cognitive process, never becomes defunct so long as the round of rebirths continues. No one, not even a Buddha or an Arahant, is exempt from experiencing the results of indefinitely effective kamma.
(iv) Defunct (ahosi) kamma: This term does not designate a special class of kamma, but applies to kamma that was due to ripen in either the present existence or the next existence but did not meet conditions con- ducive to its maturation. In the case of Arahants, all their accumulated kamma from the past which was due to ripen in future lives becomes defunct with their final passing away.
-- "Comprehensive Manual of Abhidhamma" by Ven. Bhikkhu Bodhi, p. 200-220.
As the effects of kamma is impermanent the dog would sooner or later be reborn in either lower, same or higher realms. Here the different types of kamma can come to fruition if the right conditions for them to ripen is met.