If I cast simulacrum on myself, I expend 1 spell slot to do so. Will the simulacrum still have this spell slot when it is created? Or will the simulacrum be missing the spell slot as well?
The simulacrum is created with the same spell slots that you have at the time the spell is cast
The spell explains the nature of the duplicate that is created:
You shape an illusory duplicate of one beast or humanoid that is within range for the entire casting time of the spell. The duplicate is a creature, partially real and formed from ice or snow, and it can take actions and otherwise be affected as a normal creature. It appears to be the same as the original, but it has half the creature's hit point maximum and is formed without any equipment. Otherwise, the illusion uses all the statistics of the creature it duplicates, except that it is a construct.
Your spell slots are part of your statistics, so if you cast Simulacrum on yourself, the simulacrum you create has the same spell slots that you had when the spell was cast. In particular, this means that the simulacrum lacks the spell slot that was used to cast Simulacrum, because the spell slot is expended during the casting, but the spell (like all spells) doesn't take effect until the casting is complete.
If you really want to get around this, you're going to need a trusted ally who can cast Simulacrum on you. Do this right after a long rest, and your shiny new simulacrum will have all your spell slots full. If necessary, you can scribe a scroll of the spell to enable your ally to cast it, as long as it is on their class's spell list.