You absolutely must bring your own car seat (there's no way to tell if a rental car agency's car seat has been in an accident).
I agree 100%
I traveled with my son when he was a baby and decided once not to bring a carseat. Instead I bought one for my mom and had her install it. She took it to the Fire Station and had them install it. Well, it was installed incorrectly like 80% or more carseats in the US are. People think they know how to do it but unless they're trained and experienced, they usually don't do it correctly.
And yes, you can't count on rental agencies having a carseat or having the right one to keep your kiddo safe. There are many variables, remember, and kids who aren't totally typical (extra tall or short, wider than usual, long torso, etc) need the _right_ seat, not just any seat. The current guidelines are to keep your child rear-facing as long as possible. Well, you can only do that with the right seat for your child. If you use a seat that isn't long or wide enough for your kiddo then it becomes dangerous. And if you push the limits and put your too small child in a booster seat, well, you may as well just drive around without them buckled in at all.
More details about carseat safety:
http://thecarseatlady.com/
Anyway... since it wasn't the same as my carseat I had to sit and read directions on how to install it properly before we could go anywhere. It was a challenge trying to keep my son happy while installing a carseat. Ever since then, I always bring our carseat. It makes it easier for everyone.
To me, a stroller is optional. It's handy when you go grocery shopping, since you can load it up and roll it back to your timeshare, but in the airport and out-and-about at the destination, a baby carrier is the way to go (Ergo or any mei tei type carrier). Carseats and strollers are both normally free to check on airplanes.
Agreed!
I rarely used strollers. Baby carriers are great. My personal preference is the Baby K'tan. Quicker to put on than most others and folds up smaller than most others too.
- if the baby has a "lovey" or is attached to a particular toy or blanket, bring that
Yes, this is definitely a good idea.
And you may want to get a "back-up" too and leave it at home in case the one you bring gets lost during the trip (happened to a friend of mine).
At that age - I am going to assume the baby is one of those bucket type car seats now that clip in and out of the car. These seats usually have a matching stroller that the bucket clips into also. (at 5 months old, I don't think an infant is large enough for an umbrella stroller)
Agreed that most 5 month olds aren't big enough or have the neck and spine control enough for an umbrella stroller. But there are some very nice strollers that may technically be classified as "umbrella strollers" but can lay back flat or nearly flat so that they're safe for that age baby.
Regarding bucket seat carseats, indeed this is the most common. But it's not the only option. There are plenty of other carseats that a suitable for an infant to year that are not the bucket style. Personally, we used non-bucket style because they have fewer points of potential failure. Our choice was/is this one:
http://us.diono.com/convertible-to-booster/radianrxt
Our son is 5 and still uses it
A reminder: not all carseats are approved for use on an airplane. So if you plan to use it on the plane (which I recommend because turbulence can cause significant injury in babies) then make sure your seat has the sticker for airline use. You will need to show that as you board. My experience is that about 3 people per flight will try to take the seat from you and a few here and there will ask to see the sticker before they let you use it on the plane. Also know that you must install it in a window seat and cannot be seated in or near the emergency exit rows. They may also want you to sit a certain distance away from any other passengers using special seats (other children in carseats or persons with physical disabilities etc).
More details on that:
http://www.faa.gov/passengers/fly_children/
About a crib or pack-n-play, I agree that can usually be borrowed from the resort or purchased at the destination, but you may not want to chance it.
Regarding formula, my experience was that they tested it once. Most times they just looked at it and passed it through. I will say, once they patted me down while I was wearing my son. He was sleeping and they tried not to wake him but they were unsuccessful.