What is the research design for the study I am proposing?

I am proposing an experiment in developmental psychology which asks whether the early use of decision rule X at $t_1$ (In children mean aged 9) is correlated with the use of more sophisticated rule Y at $t_2$ (Children mean aged 10 years 10 months).

I would like to know two things.

Firstly, what type of design is this? At first I thought it was a correlational design but because it is staggered by discrete time intervals now I am not so sure.

Secondly, and I had some help with this thanks to Bryan Krause, how should I report my statistics? I understand that I may be using a Chi^2 test for independence, so therefore do I simply say: ‘We will use a Chi² test of Independence to determine whether Rule X use at _t¹ is correlated with Rule Y use a t²’. Will I need to provide any additional information or run any additional tests?

Because of a classification criterion , i.e. 20/25 responses being consistent with Rule-usage, the results collected will be non-continuous.

Thank you for reading.