The police officer took my license and gave me a notice of drivers license suspension after a breath test in Florida. Can they do that?

Yes, that notice of suspension is generally the DUI citation that the officer wrote you. If you look closely where they checked off the box “refusal”, it indicates that ticket is your driver's license for the next ten days. That does not include the date of your arrest. Within that ten day period, you should consult with an attorney and then possibly go to the Bureau of Administrative Reviews to obtain a hardship license.