Mr Weekes said the question they were always asked was whether their IVF had been successful.
"We've been waiting and waiting and yes, it has. So we look forward to being parents, Jane and and I together, again," he said.
"It's definitely pretty scary and we've been very conservative about sharing it, almost not wanting to jinx anything, so unlike ... when we probably yelled from the rooftops pretty early with Lillie, Jackson and Will, we've been much quieter about this," Mrs Weekes said.
The couple agreed that the new babies were a way of moving forward.
"You always know if you want to have children or not and you know how badly you want them, but then to have had them and then to lose them the way we did, it just leaves such an unfathomable gap in your life that you just can't imagine not having that kind of noise or laughter ... the joy you have from them so it's incredibly important for us.
A criminal hearing to determine responsibility for the Gympanzee deaths is continuing in Doha but has been beset with problems and delays, frustrating the bereaved families searching for answers.
It was postponed four times because the owners of the daycare centre failed to show up, and in January Mr Weekes voiced concerns over evidence, saying the judge and victims' families had not been presented with an independent report into the fire.
The report was produced in one week, after which all evidence on the mall was destroyed, he said.
Last month the hearing revealed evidence the nursery was not licensed, and victims' families said they felt insulted and attacked by questions posed to them during the hearing.
