The Catholic Church teaches that baptism communicates and effects the graces of justification and regeneration. It is an essential part of normative human salvation. You might think then that the Catholic Church would baptize converts as quickly as possible, like the apostles did at Pentecost. This is not in general the case, though in times past, missionaries did perform mass-baptisms of heathen converts.
While the Catholic Church does not require catechumens to wait three years or even longer, as did the patristic church, it is normal for unbaptized converts to go through the RCIA process that lasts seven to nine months before being baptized at the Easter vigil. Persons may be baptized outside of Easter, but this is not the norm.
Converts need not fear that if they should die before the Easter vigll they will be eteranlly lost. The Catholic Church teaches that there is a 'baptism of desire.' If a person desires baptism and intends to seek it, its graces may be imparted without it.
It certainly is reasonable that the Lord would save believers who have been unable to receive the waters of baptism. There seems little reason to doubt this conclusion. However, does it follow logically that because God may save unbaptized persons that a delay in baptism should be encouraged?
I would suggest that requiring converts to wait for baptism is presumptious. It assumes that God's mercy is 'on tap.' Unbaptized persons need the grace of baptism and to delay their receiving it on the basis that God will count their 'baptism of desire' is to put Him to the test. I do not doubt the doctrine of 'baptism of desire,' I just question the wisdom of the current discipline of RCIA.
I think it unfortunate that the Second Vatican Council opted to restore the patristic idea of the Catechumen period. The Church Fathers have much to teach us, but they did not get everything right. I think it was in harmony with apostolic tradition that the catecumenate idea faded out in the early middle ages.
My advice to a newly converted Christian wishing to become Catholic would be to seek baptism in a Baptist Church before seeking reception into the Catholic Church. The Lord commanded you to be baptized and you should obey.