Now I don't think English poetry is any more "non-grammatical" than Latin poetry. Rather, the grammar is convoluted and ornate: it is the nature of poetry to stretch the bounds of grammar and experiment in form. This is true of Latin and English. I don't think you're better off with the Aeneid than you would be as an English novice with Shakespeare.
As a native speaker of English and a scholar of literature, there are many poems that I have to read several times carefully to fully understand the grammar (Milton leaps to mind). Now I imagine many Romans had to pause and think in order to understand some of their own poetry.
With that said, go right ahead with Virgil if that's what you want to read. I highly recommend Clyde Pharr's edition of Virgil Books I-VI. It has all the grammar aides, vocabulary, and commentary on the same page as the text, so you'll avoid flipping around. Plus, he provides helpful tools like vocabulary frequency charts, helpful introductions, a grammar reference, and pictures. It's expertly designed for people at your level.
http://www.amazon.com/Vergils-Aeneid-Bo ... 654&sr=8-1