First, no, you have not ruined the your dog for SAR.. Don't worry.
More importantly is what Carmspack brought up, and that is the IMMENSE dedication and work that goes into being a K9 handler for SAR. This is not to dissuade you, but to definitely be real and upfront. If it is an 'outlet' for the dog, then go with nose work, IPO, tracking, herding, rally or some other type of sport/work. SAR requires 1,000's of hours for human and K9 just to be mission ready, let alone to maintain and improve on those skills, which should be of utmost importance as lives are at stake.
Now, if you are aware of this and are committed to SAR, then don't worry about the pup interacting with family animals etc. However, if the dog is toy driven, I would use that time to use the toy for educational purposes rather than 'burning' the reward of the toy on frivolity. There are many many exercises that you can begin to build the hunt drive and focus the pup will need for SAR in fun short games, at home.
Hope this helps... (yes, I am a SAR volunteer with two dogs certified, in trailing, article and HRD land and water