I flew my son to Florida at 6 weeks old (cleared by his ped.). Nurse/bottle during take off and landing, if they're even awake at landing, and other than that they're fine. I did not get him his own seat, but he had one anyway. How I did this was pretty easy, I had a seat reserved for me and one for my DD3. When we checked in, I asked how full the flight was (which was not at all, I had already planned on flying at some very interesting times for just that reason) and the woman at the counter moved us into two seats in a three seat row, with an unreserved seat in between. Which became my son's seat. (Delta actually has that in their rules. Infants can either sit in your lap or in a car seat in an unreserved seat next to you without paying.) More flight tips, sit near the engine (annoying to you, but a lulabye to your infant, and if he gets mad, no one will hear him anyway) gate check your stroller, and spring for a nonstop flight if there is one available. If you are nursing, bring an extra blanket to use as a screen (or wear a big, giant cardigan) as you may well nurse the whole trip. And I mean the whole trip. Change diapers right before boarding just in case (although I have done it in an airplane bathroom, it can be done, but it would help if I were a 16 year old Romanian gymnast) and when you first sit down in your seat, take out all the flight magazines and safety rules and replace them with things you will need, bottles, diapers, wipes, extra pacifiers, toys, blankets, spit rags and plastic garbage bags (I use the grocery store kind) because once you stow that diaper bag, even if it's just under the seat, you will not see it again before you land. Murphy's law of Diaper Bags.
When at the parks, make good use of the Baby care centers and the child swap. You ride the ride, DH waits with baby at the loading area. You get off, and the CM's will allow you two to switch. If your child is light/sound sensitive, try to stay away from fireworks, etc. Invest in a good infant carrier like a Baby Bjorn (easy on, easy off) for slow rides that you can bring your infant on, like Peter Pan and Snow White, even Haunted Mansion and bus trips (also works great on the airplane).