Old Fashioned Rolled Oats make for the best kind of granola. Using a hearty oat allows homemade granola to crisp up nicely, giving it a good crunchy texture. If really wanting to use a quick oat you can.
But I would suggest using a mixture of an old fashioned oat and quick oat, with no more than half of the oat being a quick oat. Using too much of a quick oat will cause your granola to be soggy and limp.