You could always reach out to the admissions team at SRUC with this question.
At a quick look, it seems as though Stirling animal biology requires BBB in A levels or AABB in highers, whereas SRUC vet nursing requires BBB in A levels or BBBB in highers, so it looks like if you meet entry requirements for the biology course you would meet them for the nursing course, without the extra degree. The biology degree might help you gain valuable knowledge for the nursing degree. It might be worth checking with SRUC if they would have an entry requirement based on a previous degree (i.e. they may stipulate a grade).