Learn Dutch: Welk konijn zullen we adopteren? - Which rabbit shall we adopt?

Because konijn is a neuter word (het konijn). When you ask 'which' about a singular het word, you drop the -e and use welk. For de words and all plurals, you use welke.

Could I ask wat voor een konijn instead?

You could, but it changes the meaning. Welk konijn asks you to choose a specific rabbit from a group. Wat voor een konijn asks about the category or breed ('What kind of rabbit?').

Why does adopteren go at the very end of the sentence?

This sentence uses the helping verb zullen (shall). In Dutch, a helping verb takes the active verb position, but it pushes the main action verb (adopteren) all the way to the end of the sentence.

Is zullen we a common way to suggest something?

Yes! The phrase zullen we is the standard Dutch way to make a suggestion about doing something together, just like saying 'shall we' or 'should we' in English.