Technically they should be able to lay eggs.
A common misconception is that Daenerys' dragons are all males. That is not true.
Dragons do not have a fixed gender1. They can change to male or female at will.
What fools we were, who thought ourselves so wise! The error crept in
from the translation. Dragons are neither male nor female, Barth saw
the truth of that, but now one and now the other, as changeable as
flame. The language misled us all for a thousand years. Daenerys is
the one, born amidst salt and smoke. The dragons prove it.
AFFC - Samwell IV
But we do not yet know when do Dragons become capable of laying eggs and reproducing.
Daenerys' dragons are a couple of years old, so they could be considered children among a species which lives for centuries.
Presumably, They should be able to start reproducing at least after 10-20 years. Syrax was born in reign of King Jaehaerys I (Implied as Rhaenyra who was born in 97 AC during reign of the Old King named the young dragon, which implies it was a hatchling and had no previous rider or name). It grew up during reign of King Viserys I and known to have laid eggs during that period. Viserys reigned from 103 AC to 129 AC for 26 years. If we assume that Syrax was born in 97 AC2 (As it existed back in the day of Jaehaerys I), Syrax must have been at least 10-20 years old when it first laid eggs in reign of King Viserys. It can't be emphasized enough that this is merely my speculation, Syrax could have been younger (Could be more like <10 but that seems wrong given that dragons must have some stage in their early life when they are incapable of reproducing like all animals).
The secrets of Dragonkind were lost when King Baelor ordered Septon Barth's Unnatural History to be burnt through out the Kingdom. So as of now, their nature is a mystery.
So Spake Martin
GRRM says the following on Draconic Reproduction and genders:
Q: [Are dragons male, female, hermaphroditic, or is there something magical involved in their reproduction?]
GRRM: Sexing dragons is difficult. More in future books.
SSM: DRAGON LIMBS AND GENDER, VALYRAIN WEAPONS, AND MAESTERS’ CHAINS
1. There are those who dispute it but Barth was the leading expert in Dragonlore in Westeros and he actually had a first hand chance to observe dragons during reign of Jaehaerys I. Maester Aemon is also a great scholar and if he agrees with Barth instead, So do I. Munkun only saw the extinction of Dragons and the only Dragons he ever observed were sickly and dying. Thomax on the other hand, we do not know when did he live so we can't speculate on accuracy of his views.
2. 97 AC because that's when Rhaenyra was born, during the reign of Jaehaerys I. It was a custom of Targaryens to lay dragon eggs in cribs of new born Targaryens, and it would hatch and grow with the child.