This is really up to you. In 3.5, you could animate anything, to a limit.
In 5e, you can specifically only target Humanoids by RAW, however this is D&D so never let that stop you. If you expect to run into times when you aren't going to be seeing humanoids (or just because you want to) don't let the RAW stop you.
A Skeleton is a CR 1/4 creature.
Animate Dead allows you to animate one humanoid worth 1/4CR
The Necromancer subclass allows one additional humanoid for a total of 1/2CR.
Casting the spell as a higher level allows you to creature 2 more undead (so another 1/2CR).
You could, within your purview as DM, simply allow your necromancer to animate the corpses of a set amount of CR worth of creatures.
A Sabre-tooth tiger is a CR of 2, which means you would need to cast the spell at level 5 OR as a necromancer at level 4 and you could then animate the sabre-tooth tiger.
Now you have an undead sabre-tooth tiger equal in CR to 8 skeletons, which sounds fair to me but you have another problem, Skeletons and Sabre-tooth tigers have unique abilities and you would want to make sure your undead sabre-tooth shows some undead traits. For this i would make sure you remove some of the sabre-tooth traits (Keen Smell, Pounce) and replace them with undead traits (Immune poiuson, Exhaustion, Poisoned) and if its a skeleton give it vulnerability to bludgeoning.
And just repeat for whatever else you want to do. Its not a easy solution but it is simple, it just requires a little math and some tweaking and i think its a VERY good idea for necromancers (maybe JUST necromancer subclass even) because.. what if you are somewhere where you don't see humanoids, what if you want to be creative? You should reward creativity.