No, unfortunately, having a child is not a exception from paying taxes on your early 401(k) withdrawal.
However, you can take a withdrawal of up to $5,000 per child for expenses associated with birth or adoption penalty free. Additionally, you can exempt medical expenses (over 7.5% of your adjusted gross income (AGI)) that you incurred during the year from the early withdrawal penalty.
To summarize, you have to pay income taxes on the withdrawal but some (or all depending on how much you withdrew) will be exempt from the 10% early withdrawal penalty.
Here is some more information: Are there exceptions to the early distribution penalty on an IRA?
