Marriages between non-baptised persons or a non-baptised with a baptised are considered to be valid and natural marriages. They are however not sacramental, but the moment the non-baptised persons are baptised the marriage automatically becomes sacramental.
There is no need for a blessing or convalidation in a Catholic Church. A Catholic is bound by the Church law and have to be married in the Church by a priest or deacon. If the Catholic is married by a JP or any other person than a Catholic priest then this marriage is not considered to be valid. The Church can in certain circumstances give dispensations regarding this rule.
Persons who are not Catholic are not bound by Church law and can marry according to their custom and it will be a valid and natural marriage.
The moment your wife was baptised your marriage became a sacramental one. Your marriage are considered to be a valid and sacramental marriage by the Catholic Church. Of course, only if this was the first marriage for both of you.
If any of you were married before, even a brief and childless one, and were divorced your current marriage may not be valid and you have to talk to a priest about how to solve this situation.
I was baptised as an infant into the Lutheran church of Norway. I married a Muslim (non-baptised) in a Muslim ceremony. We were years later divorced. Last year when I started my journey towards full membership in the Catholic Church I had to solve this marriage situation since I wanted to marry my fiance in the Catholic Church.
Since my marriage was not sacramental, but considered to be a natural and valid marriage it can be dissolved. In my case as a baptised married with a non-baptised the Pope can dissolve the marriage in “Favour of Faith”. This is called a “Petrine Privilege”. I got my Petrine Privilege in May and is now free to marry my fiance.
I would talk to a Catholic priest about your and your wife’s wish to look into the Catholic Christian faith. He will be able to guide you and give you the correct answers. The RCIA (Rite of Christian Initiation for Adults) programs is starting in these days. You are not under any obligation to become a Catholic Christian and can use all the time you need to decide if you want to be received into the Church.