This is nothing to be nervous about. It happens all of the time, and parishes are quite used to answering these questions. For most places, the children wear whatever you think appropriate. Sacramental preparation classes or meetings is normally where you’d have these kind of questions answered. Generally speaking, though, baptism pouring the water over the head is still the most common. If baptism by immersion were the norm in your parish, and not simply an option you could ask for, I’d think someone would have told you by now. (Our kids were immersed as infants, but it was an option.)
There is no etiquette that says they must (or must not) arrive for their baptism in particular kinds or colors of dresses. (You wouldn’t dress either like a tart, of course, meaning, in imitation of immodest grown-up females whose clothing is chosen specifically to transmit loose morals, but I hope that goes without saying…)
No matter what either child (or even an adult) wears to church for the occasion, the parish normally provides a ritual “white garment” that is put on over the regular clothing for the purposes of the ceremony. In our locale, this is typically a white tunic made of handkerchief-weight cotton or linen. These are very simple, and if the fabric used does not tend towards fraying, they are sometimes are not even hemmed at the edges. Because of this, it doesn’t matter if the candidate for baptism comes to church in white garments or not.
I hope that when you say “we plan to have them baptised”, you have a date with the parish already, and not just an idea to have it done on short notice at a regularly-scheduled monthly baptism. At parishes in our archdiocese, for the younger child you and the children’s godparents would typically need to attend either meetings with the pastor or his designee or else go through formal pre-baptismal classes for parents having a first baptism. The older child, though, having reached the age of reason, so that this is her decision would typically be received into the church through RCIC (Rite of Christian Inititation for Children). Whether she would receive her First Holy Communion on her baptism day or waits to make her First Holy Communion with the children her age doing it this spring or next depends on where you are and consideration of what is best for her particular case by your pastor, but I would expect she would normally do so on her baptism day.
Sometimes, Catholics who have not received any sacraments except baptism also go to the same classes as catechumens (that is, RCIA). In our parish, some receive First Reconciliation during Lent and then Confirmation and First Holy Communion on Holy Saturday. (At some places, Easter Vigil initiates catechumens only, and the baptised finishing initiation are taken care of at another time.) Again, it depends on local custom, the number of initiates, and your pastor’s sense of what best fits your case, but I am surprised that you were not highly encouraged to have your own initiations finished immediately when you asked to have your children baptised. How do you raise your children in the faith, when you have not been fully initiated yourselves?
In any event, it is nothing to get in a wreck about. Do your best to have this done as early as the parish will let you, and you will be OK.
and your older daughter would likely be baptised with other kids near her age.