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?

Well! You may have problems and may not. It all depends on individual's biological clock. Some don't even face any difficulty conceiving even at 40 and some have problems even at 30. So, it is all about how ell your eggs respond and your partner's sperm count. But in any case you can visit a doctor and rest your doubts.