Thank you for your question. The Middle District of Florida does not have a rule specifically providing for a stay of an order transferring venue.
First of all, you should probably file a Motion to Reconsider the Motion to Transfer Venue before you file for an appeal. If you have a reasonable excuse as to why you did not answer the motion, then the court might rehear it.
Second, there is no Federal Rule of Civil Procedure which specifically grants a party the right to stay a court's decision to transfer venue.
Rather, you should cite Federal Rule of Appellate Procedure 8 as your authority:
FRAP 8. Stay or Injunction Pending Appeal
(a) Motion for Stay.
(1) Initial Motion in the District Court. A party must ordinarily move first in the district
court for the following relief:
(A) a stay of the judgment or order of a district court pending appeal;
(B) approval of a supersedeas bond; or
(C) an order suspending, modifying, restoring, or granting an injunction while an
appeal is pending
An appeal of a motion to transfer venue is a mandamus action.
The party opposing transfer is, at a minimum, entitled to notice and an opportunity to be heard, and a failure to afford such an opportunity will be remedied by mandamus.
Wood v. Zapata Corp., 482 F.2d 350 (3d Cir. 1973)
Mandamus is issued to prohibit transfer only if the district court grossly abuses its discretion. See In re Tripati, 267 U.S. App. D.C. 58, 836 F.2d 1406, 1407 (D.C. Cir. 1988) (per curiam)
Welch v. Moore, 1995 U.S. App. LEXIS 19986 (D.C. Cir. June 19, 1995)
Also, see the following for guidance in the 11th Circuit Appellate Courts: http://www.ca11.uscourts.gov/documents/pdfs/BlueAPR09.pdf
Please let me know if you need further assistance.