My son (age 5) is the same I so bought him gloves, pads, bag and helmet from SD (all very cheap) to wear if and when he wants when i play on a saturday, because he wanted to be like dad. But he doesn't wear any of them for training in my u7's kwik cricket side or playing at home, although I do sometimes find him wearing his box around the house:)
Kit is definitely a lot cheaper (all the above for £25 including bag) than when I was a kid, I remember as a youngster going to cricket with my parents and using my dads old GN scoop, cut down of course. I also recall one of my mates who's dad also played in my dad's side having a St Peter bat.