Under federal law (18 U.S.C. § 922(g)) it is illegal for any person who has been convicted of a crime punishable by imprisonment for a term exceeding one year to ship, transport, possession, or receive any firearm or firearm ammunition. The term The term “crime punishable by imprisonment for a term exceeding one year” does not include—
(A) any Federal or State offenses pertaining to antitrust violations, unfair trade practices, restraints of trade, or other similar offenses relating to the regulation of business practices, or
(B) any State offense classified by the laws of the State as a misdemeanor and punishable by a term of imprisonment of two years or less.
18 U.S.C. § 921(a)(20)
Note the key word punishable that I emphasized. That term means that if the maximum penalty for the crime is imprisonment for more than one year (or two years if it is a state offense that the state calls a misdemeanor) then the person is prohibited from possessing any firearm or firearm ammunition under federal law even if the actual jail or prison sentence imposed was one year or less.
In your case, you plead to a burglary of an occupied dwelling charge in Georgia. Currently that is a state law felony offense subject to a term of imprisonment of no more than 20 years and no less than one year on a first offense. You plead guilty and took deal for a 3 year sentence, two of which were suspended with one year to serve and you got out a bit earlier than the one year (presumably for good time). The problem is that while your actual time in jail or prison was a bit over 10 months, the crime is punishable by a term of up to 20 years in prison, i.e. the court could have imposed a sentence of 20 years. The details of the max sentence for the crime may have been a bit different when you were sentenced years ago, but your sentence confirms that the crime was at least punishable by imprisonment for 3 years. That will prohibit you from possessing a firearm or firearm ammunition under federal law unless you get relief from that conviction (e.g. a pardon from Georgia’s governor, etc).
The Florida statute would appear to work much the same as the federal one. You were convicted of a felony in Georgia that was punishable (i.e. the max time the court could have imposed) by a term of imprisonment of more than one year.
In short, it is the max time the court could have imposed that counts here, not the actual time you ended up serving inside.

