hi...If I was looking for a bunch of choices, I would google "pet friendly orlando vacation rentals" and the results will be primarily folks looking for weekly rentals. Look over the properties and check "availability calendars" if they have them on the web sites, and make sure February is wide open before you contact them. Pick out the ones that are available and appeal to you.
Draft a template email that you can can cut and paste if you have lots of choices and send each owner a personal email. We do this for 3 months and have had great luck (no pets, however, so lots more options).
You might want to wait until about August or September when the chance of the owner renting out more than two weeks gets slimmer and they are willing to look at month for a discount.
Advice is cheap, but do expect to get a considerable discount for taking the whole month of February. For the owner, this is guaranteed income, no weekly cleaning fees, and a chance to rent to you next year.
Good Luck...let us know if more questions...