First of all, 'religion' is difficult to define. On dictionary.com, we have:
religion /rɪˈlɪdʒ ən/ • a set of beliefs concerning the cause, nature, and purpose of the universe, especially when considered as the creation of a superhuman agency or agencies, usually involving devotional and ritual observances, and often containing a moral code governing the conduct of human affairs.
However, wikipedia suggests a much broader definition:
A religion is an organized collection of beliefs, cultural systems, and world views that relate humanity to an order of existence.1
1: While religion is difficult to define, one standard model of religion, used in religious studies courses, was proposed by Clifford Geertz, who simply called it a "cultural system" (Clifford Geertz, Religion as a Cultural System, 1973). A critique of Geertz's model by Talal Asad categorized religion as "an anthropological category". (Talal Asad, The Construction of Religion as an Anthropological Category, 1982.)
I will be taking the first definition as it's what is most commonly considered to be religion. Now let's have a look at your question.
Could we consider his world of ideas a divine world? Isn't that the same as the world of God?
In Platon's system there are perhaps two objects that could classify as a god: the sun and the Idea of the good. Note that both are fixed in the sense that they don't do anything apart from what they always have done and always will do (which could be a key difference with common world religions nowadays).
I don't think Platon would speak about the world of Ideas as of a divine world. He actually strongly emphasises that it is a definite and reachable entity. In the allegory of the cave in The Republic, book 7, 517B (English on the right), he writes:
And if you assume that the ascent and the contemplation of the things above is the soul's ascension to the intelligible region, ...
That intelligible region is in Greek 'τόπον τῆς ψυχῆς', meaning 'place of the ψυχῆς'. This ψυχῆς, from ψυχὴ, has an incredibly long dictionary entry, meaning among other things 'spirit', 'breath', 'life', 'mind' and 'consciousness'. The LSJ dictionary has one specific section (V) for philosophical uses, and in V.3 we see that in Platon this word may also mean 'the immaterial principle of movement of life'.
All this suggests that the world of Ideas is a place that is reachable (by philosophers). This is different from the notions of divine worlds we find in most religions nowadays.
Probably you could take Platon, scrap the parts you don't like and add some things of your own, possibly adding a god-entity (or using the sun or the Idea of the good for that), and building a religion around it. But that does not seem to be Platon's idea.