Two issues, I think Cathedral is more physically demanding than Huntington. It is essentially a 1 1/2 mile vertical scramble. As far as exposure, if your 7 year old isn't afraid of the vertical on Huntington he/she should be able to handle Cathedral.
If you're concerned, you may want to consider ascending the Saddle Trail to Baxter Peak and then descending the knife edge and down either the Dudley or Helon Taylor from the summit of Pamola. The biggest challange here will be getting down and up the Chimney. The Taylor is long and seems to drag on forever, but it is the easier of the two.
I think the biggest problem for a seven year old is there are areas on both Dudley and Cathedral where a long reach is required to go up, around or over large boulders. You should obviously be prepared to assist.
Good luck, hope this helps.
I hike this area every year. As I think about this, I can honestly say that I have rarely seen children as young as 7 on most of these trails. IMO, there isn't anything in NH that is as demanding as Katahdin and the surrounding area.