Do you think $10K is enough to have saved for baby?

Our baby is due in May and we have about $7.5K saved up now. We are hoping to have between $10K-$12K saved by May. This would be to cover supplies, anything our insurance doesn’t pay for (Deductible is $3K but we are thinking it will almost cover everything), any extra help with daycare we might need if the month is a heavy spending month, and general emergency money. I also have 6 weeks unpaid maternity leave which equates to about $3300. What do you think? We will continue to put $400-600 away every month as well once baby boy is here.