Do I need separate inspectors for property and pest inspections?

Not when dealing with Grounds Home Inspections.
David Grounds is a Certified Building Inspector, a Certified Pest Inspector, a Certified Pest Controller and a Registered Builder
Some may tell you that you need different inspectors but in reality you will get a higher level of inspection if the one person handles all aspects of the property inspection. For example, a dedicated pest inspector may be inclined to push you towards unnecessary chemical pest treatments to generate sales. Or a house inspector may not be aware of the dangers and hazards certain pests may have upon a buildings structural integrity.
Many inspectors do not have this cross inspection knowledge.