Need Help w/ Japanese Poetry?

I began researching Japanese mythology and poetry in order to compose a waka/tanka [5-7-5-7-7 syllable-lined poem]

I have received some assistance from a foreign exchange student I met, but would like 2nd opinions and further editing/revision.

It is a simple poem based on the God and Goddess Tsukuyomi [moon god] and Amaterasu [sun goddess]

English concept:

The morning sun shines

And in the evening she wanes

At night she is gone

The moon has come out to play

He wonders where she has went

Rough Japanese translation:

朝日照る - - - - - Asahi teru

夕方に衰え - - - Yūgata ni otoroe

夜にいなく - - - - Yoru ni inaku - - - - - - [to be read/said as "Yoru ninaku"]

月来る遊んで - - Tsuki kuru asonde

- - -

As you can see, I would like the odd lines to rhyme, and the even lines to rhyme; this means that the 5th line needs to end w/ -u.

I figured that trying to translate "He wonders where she has went" directly would require too many syllables, and so I am trying to use the phrase "Where did you go?" - which can then indirectly mean "He wonders where she has went."

I have found a few phrases

どこに行く - - - - - - - - doko ni iku?

どこへいきましたか - - doko e ikimashita ka?

どこに行ったか - - - - - doko ni itta ka?

I was wondering, for the sake of a 7-syllable ending w/ -u, if this would poetically make sense

どこに行った行く - - - - Doko ni itta iku?

Please, I am asking for your input, ideas, changes for grammar.

- Thank You