Is there a need of Point interpolation before proceeding for gaussian smoothing of an incomplete distribution?
Irregularly sampled data need not necessarily be interpolated prior to smoothing. You can try to smooth your data in the following way:

$$y(t_n)=\frac{\sum_{k}g(t_n-t_k)x(t_k)}{\sum_{k}g(t_n-t_k)}\tag{1}$$

where $t_n$ are your sample times, $x(t_n)$ are your data, and $g(n)$ is your smoothing kernel. Note that $t_n$ need to be integers (as in your example), which is no restriction, just a matter of formulation. Since $t_n$ are irregular, you do not always use all values of the chosen kernel $g(n)$, but this is compensated for by the normalization in (1). The kernel width has to be chosen such that the kernel always covers at least several of your irregularly sampled data. The smoothing in (1) is also used in the Nadaraya-Watson estimator.