This lack is currently intentional for several reasons.
Don't migrate junk!
That's the first and biggest rule when it comes to migrating questions. If the quality is low, the question is borderline off-topic on both sites or it's a "X Y problem" where OP writes X (that belong on a different site) but actually means Y (that belongs here) then a question shouldn't be migrated at all.
To ensure these criteria, migration is per default an action only moderators can do. The process may also include checking with the OP what the actual subject of their question is and asking the mod team of the target site if they'd accept the question.
Migration paths
To reduce the workload of mods, each site can define up to 5 migration paths. This gives non-mod users the possibility to vote to migrate a question without forcing a mod to take action.
Before such a migration path can be defined, the site has to show that there is a history of many questions having been successfully migrated to the target site (without being closed). As of now, Pets doesn't have any clear migration paths at all and the total number of successfully migrated questions is negligible.
If you think a question should be migrated, please flag the question for mod attention and leave a short comment.