Some babies start to experience separation anxiety around six months when she understands the concept of object permanence and knows that you still exist even when you are not by her side. Separation anxiety typically peaks around 8-10 months.
Try to resist the urge to slip out unnoticed. It is always better to take the time to say goodbye and tell her when you will be back so you build trust.
Explain transitions to her so she begins to understand what is coming next. This also adds to her vocabulary and language skills.