Q: I left my old company on June 29th started with my new company on July 2nd I am leaving them to accept a new job that fits my needs. I would like to get cobra for just my 4mnth old daughter how can I do that. A As long as your child was on the policy before you left your old job, the child will be eligible for COBRA continuation. On the election form (that you will get from your employer) you will be able to elect who you want to continue the COBRA coverage. The employee does not have to accept COBRA coverage for themselves to get their spouse or dependent children covered under COBRA continuation.