I am so sorry for the loss of your child's father. This is not a probate question, it's a workers compensation question. I suggest you repost the question with a workers compensation tag. I also suggest you consider hiring your own counsel, if you don't have one already, to try to maximize the benefits for your child.
The contents of this answer should be considered friendly advice, not legal advice and the answer should not be construed to constitute an attorney-client relationship. If you'd like actual legal advice, call me at 954-567-4100. Also, if you liked this answer did, be sure to click the thumbs-up button
You need to concentrate more on Paternity than checks. The birth certificate, pictures of Dad with the kid, Group pictures, relatives that confirm him as the Father. There is typically a presumption that a minor child is a total dependent, but your child has a lot of money at risk. A FL Workers' Compensation Attorney would be a VERY good idea to make sure nothing goes wrong.
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Under Florida workers' compensation law, your child is entitled to dependent benefits as long as you can show that the decedent injured worker was his father regardless of whether you and his father were ever married. However, the decedent/father's death must have resulted from the workers' compensation accident within one year thereafter or follow continuous disability and results from the accident within five years thereafter. If that is the case, his employer's workers' compensation insurance carrier is responsible for actual funeral expenses not to exceed $7500 and his spouse and children are entitled to certain compensation disability payments, the amount of which is dependent upon whether there is a spouse and how many children or other heirs there are. There are several excellent workers' compensation attorneys in the Orlando area and you should consult one.
Disclaimer: the above does not constitute legal advice and is only an opinion of the author as to current law. You should consult an attorney with questions about your particular situation.