As the events occurred in 1800 I think it would be fine if you named names, which may be usueful if anyone wants to try to help.
A later arrival is possible but you would expect all sorts of permissions to be needed (and a paper trail) to enable convict to be reunited with child, so probably unlikley. Someone I researched asked for his wife to be allowed to come out but this was refused, so I would expect a child to be refused especially if she had relatives and possibly a father back in England to look after her. With mother a convict, child would be a burden.
She could have travelled with relatives as part of another family group.
Sandie’s suggestion of her being pregnant on the boat is probably the most logical.
What is AJCP?