To determine the correct heads for the questionnaire, we must align them with the objective: determining the feasibility of setting up a family-oriented vacation resort.

Let us evaluate each given head:

• 1. Size of family: Highly relevant. Since the proposed resort is "family-oriented", knowing the average family size of the visitors is essential for planning room layouts, amenities, and recreational activities. This directly impacts the feasibility and design of the project.
• 2. Budget: Highly relevant. Understanding the visitors' vacation budget is crucial for determining the financial viability of the resort, deciding the pricing strategy, and identifying whether the target demographic can sustain the business.
• 3. Number of earners in the family: Irrelevant. The actual vacation budget (Head 2) is a direct and sufficient indicator of a family's spending capacity. Asking for the number of earners is unnecessarily intrusive and does not provide direct value for a feasibility study.
• 4. Food allergies and dietary restrictions: Irrelevant at this stage. This is micro-level operational data collected from guests when they actually book a stay or dine at the restaurant. It does not help in determining the macro-level feasibility of setting up the resort itself.

Therefore, only Size of family and Budget are appropriate for the feasibility questionnaire.

Hence, the correct option is 1 and 2 only.