Once my seedlings of any plant get their 2nd to 3rd set of true leaves I transplant into a larger pot .. not too large though. When you transplant yours, make sure you break the peat pots vertically on the side about 8 times around so the roots can easily grow without having to punch through the peat pots.
I keep the soil on the wetter side of moist but NOT wet at first and start out with morning sun and afternoon shade. After a week or so and things are looking good, I increase the sun time until it's essentially all day. All hibiscus like full sun for a minimum of 7 - 8 hours and damp feet.
