Also you probably already know this, but for anybody reading, it is not safe to give a rabbit plants that have been mowed (because of the chance of getting gasoline on it) and if it has had any pesticides or fertilizers or fungicide.
That is barley, or possibly wheat. I understand that seed and grains should be avoided. The rest of it is ok. Both of these grains sometimes get mixed in lawn grass seed. Sometimes they are used for erosion control on roadsides for their fast growth. Sometimes they simply spill out of trucks in transit.
Compare to Foxtail (which actually comes in 6 or 7 varieties)
Foxtail seed and seed STEMS should be avoided. They can injure the mouth and intestines.
So I have some foxtail growing in my yard. I took the time this morning to feel the stem. While the reports I read on foxtail in pasturage talk about the stems having barbs I could not sense any. The awns are rather prickly. I can see how they would injure soft mouth parts. The stems could splinter, specially when they dry out. The foxtail in my yard is still at a stage prior to dough so I can't say empirically yet.