I looked for a life jacket for my young baby and didn't find anything that would have been comfortable while playing in the heat for a half hour.The one we ended up with is sold at REI, I remember that, at least. Whether one would work well in the circumstances you're describing would depend on your LO and how willing he is to wear a life vest while playing.
I think it's a good idea to check out the pool before worrying too much. While I don't agree that all pools have a similar design (they don't in my area), what I think a lot of them do have in common is being fairly family friendly. I'd wager a bet that there is a play structure, a baby pool or at least a picnic area where you can pass the time.
If there isn't, passing a half-hour on a pool deck with three kids would kill me too - mainly because of the younger children wanting to get in the pool too! I'd probably drop-off and do an errand or take a walk with the other kids.
Side note - we're on our third summer of having an older child and and and infant/toddler. It's been interesting - each summer poses different challenges. My younger is now 2 and it will be interesting. In many ways easier because she can tag along on so many more things but the new challenge is that she is starting to feel left out... poor thing! To make matters worse, our pool only allows children 3+ in "the big pool" and doesn't allow older children in the baby pool. My two kids can't swim together at all. Oy!
On pool safety, the thing that stuck for me the most over the years is how often drowning is a silent thing - which is scary! But, I have to say that I don't think an 11 month old falling in the pool is all that big of a deal - not with the mom right there. I think it would be scary but not a life-threatening..and maybe a good education for your LO. This is based on absolutely NO research whatsoever. ;-)
One more thing...
My yonger's first swim lesson did A LOT of pool-side safety for the kids. They made them fall into the deep end, made them lunge for the wall and get to safety before learning to swim and etc. I think a good first swim class should have this!