I am 32 years old, married for 1 year, and don't want to have kids for another 2 years. Will I have difficulty conceiving later?

With age and hormonal changes it is believed that conceiving at a later age becomes difficult. but that does not mean you will surely have a problem. It depends on your system at that time. Some women do not have a problem conceiving into their 40's and some have a problem even in their 20's. So you need not stress about it too much and consult your gynaecologist about any doubts you have.