Here is the applicable Criminal Code provision:
Failure to stop at scene of accident - Criminal Code of Canada section 252
252. (1) Every person commits an offence who has the care, charge or control of a vehicle, vessel or aircraft that is involved in an accident with
(a) another person,
(b ) a vehicle, vessel or aircraft, or
(c ) in the case of a vehicle, cattle in the charge of another person,
and with intent to escape civil or criminal liability fails to stop the vehicle, vessel or, if possible, the aircraft, give his or her name and address and, where any person has been injured or appears to require assistance, offer assistance.
(1.1) Every person who commits an offence under subsection (1) in a case not referred to in subsection (1.2) or (1.3) is guilty of an indictable offence and liable to imprisonment for a term not exceeding five years or is guilty of an offence punishable on summary conviction.
Offence involving bodily harm
(1.2) Every person who commits an offence under subsection (1) knowing that bodily harm has been caused to another person involved in the accident is guilty of an indictable offence and liable to imprisonment for a term not exceeding ten years.
Offence involving bodily harm or death
(1.3) Every person who commits an offence under subsection (1) is guilty of an indictable offence and liable to imprisonment for life if
(a) the person knows that another person involved in the accident is dead; or
(b ) the person knows that bodily harm has been caused to another person involved in the accident and is reckless as to whether the death of the other person results from that bodily harm, and the death of that other person so results.
(2) In proceedings under subsection (1), evidence that an accused failed to stop his vehicle, vessel or, where possible, his aircraft, as the case may be, offer assistance where any person has been injured or appears to require assistance and give his name and address is, in the absence of evidence to the contrary, proof of an intent to escape civil or criminal liability.
And under the BC Motor Vehicle Act:
Duty of driver at accident
68 (1) The driver or operator or any other person in charge of a vehicle that is, directly or indirectly, involved in an accident on a highway must do all of the following:
(a) remain at or immediately return to the scene of the accident;
(b ) render all reasonable assistance;
(c ) produce in writing to any other driver involved in the accident and to anyone sustaining loss or injury, and, on request, to a witness
(i) his or her name and address,
(ii) the name and address of the registered owner of the vehicle,
(iii) the licence number of the vehicle, and
(iv) particulars of the motor vehicle liability insurance card or financial responsibility card for that vehicle,
or such of that information as is requested.
It appears the driver breached these sections by failing to give his name and address.
While there is a duty to render assistance to an injured person, there is no such legal duty in respect of an injured animal under the Criminal Code. It could be argued under the MVA that all reasonable assistance MIGHT extend to helping with an injured animal but I doubt that a court would find that transporting the injured dog would fall under that provision.