Grumman AA5 pilot reported unstable approach and landing resulted in momentary loss of control and a prop strike.

Narrative

Aircraft X suffered a prop strike upon landing at ZZZ today around XA40. Active runway was XX; but they had closed it temporarily for an FOD search. I was re-cleared for XY on a right base. Winds were 290 at 8 knots. I crossed the threshold a little fast (~80 mph) and bled the speed down as I floated. I was on centerline with left rudder in; and I put the right main down first with the wind from the right. The left main came down just as I came up to the XY x XX intersection. I went airborne again (about 3-4 feet) and porpoised twice. I should have gone around after the first bounce. I had plenty of runway left; and I didn't force the plane down. I don't know when the prop struck the ground; but I did not feel the prop strike impact nor did I feel any new vibrations in the plane while taxiing. I didn't notice the damage until I did my parking walkaround.Overall; the day was a little sporty between 2000 and 3000 feet; and I thought the crosswind was within my personal minimums. My touch and go at ZZZ1 was clean. Winds there were calm below 1000 feet. I am new to the airplane and need more training in this particular aircraft - especially in crosswinds.Contributing factors were inexperience landing in crosswind and having too much speed in over the runway and at touchdown.