一会 vs 一下 vs 一时 vs 一时半会 vs 片刻
You would say

我要去小睡片刻 or 我要去小睡一会儿

Other expressions you have are not normally used.
You could also say

我要稍微睡一会儿


All the phrases you have can refer to a short interval of time in certain context, but they can have different meanings, 一下

一下，a short interval of time, for example, 灯一下又亮了
一下，once, for example, 你过去打他一下
一下，sudden, for example, 天一下就黑了

一时 has the following meanings

一时，a short interval of time, for example, 你别一时想不开
一时，a period of time, for example, 此一时彼一时
一时，at the same time, for example, 一时间，箭、弩都发射出去

And the others

一会，a short interval of time, for example, 我要出去一会
一时半会（儿），a short interval of time, for example, 他们一时半会儿还回不来
片刻，a short interval of time, for example, 请稍等片刻

I am only listing the common meanings and although they could have same meaning, the way you use them could be different and that is why I included the examples.

Adding 儿 after 一会 would not change its meaning, it just sounds more natural and is highly recommended. However, there is no such use of adding 儿 after 一下。