We first took LO when she was 8 weeks. We were in for 20 minutes, but then they were pretty lightweight for their age. (definitely nowhere near 12lbs)
We were informed by Waterbabies and other swim companies we contacted that as long as their umbilical cord had dropped off and sealed that they could swim. Obviously if they were very small they would need to have a full body wetsuit and probably wouldn't be in for more than 20 minutes.
We started LO with Waterbabies when they were 12 weeks old. They initially weren't sure but we continued on with them. They love water now and when we go swimming in the public local pool loads of mothers comment on how confident she is in the water. We barely have to support her and if/when she goes under its no problems at all. she just bops back up. She can also easily hold herself up at the pool edge as she grabs on and puts her legs against the wall. All things taught in the lessons. (She's now 14 months)
The thing with the concern about jabs was from when the Polio vaccine was a live vaccine, when it used to be given orally on a sugar cube as it could potentially be passed about via vaccinated persons waste. This won't happen anymore given its not given the same way.
As long as the baby doesn't get too cold, so either dressed up warm or the waters warmer than a 'standard pool' there isn't really a minimum age (other than umbilical cord healed) but time will likely only be 10 minutes for a young baby