Hi Sherri Your vase is probably end of the 19th/ beginning of the 20th century. These handpainted vases seem to have been made in the UK, in Continental Europe and the US.
Yours seems unusual in that it is cased, can we have a picture of the top rim. Most of those I have or have handled are in coloured 'milk' glass rather than cased. I think this and the unusual rim decor may help with id.
These vases are mould blown, i.e., blown into a mould to create the shape.
Most are hot enamelled, i.e. painted and then reheated, as I think yours is. Other glassware is cold enamelled, but this is thicker and rougher feeling. If it's been reheated its much less easy to feel the edges, especially on the thin layers. The difference is not easy to describe but it's fairly easy to see.
I wouldn't worry about the base, some are neat, some aren't. Yours doesn't look to have a rough pontil mark but it may have been ground down to make it stand level