Certainly the 35th Regiment of Foot were stationed on Malta during 1789-1801 and beyond.
You could try and locate Regimental Muster Books and Pay Lists [may be available on film via LDS Family History Libraries] but there are quite a number of Marriage and Baptism records on the Malta Family History site and a contact that could prove useful and I’m sure they would be interested in any proven connection you have. See http://website.lineone.net/%7Estephaniebidmead/index.htmhttp://website.lineone.net/%7Estephaniebidmead/index.htm , to search indexes scroll down home page click Indexes RH side and there’s more after that page, again scroll down and click Next Index.
A point to note though so you don’t build yourself any unnecessary walls, is that at the time of Mary Reed’s birth the 35th was known as the 35th [Dorsetshire] Regiment of Foot, then in 1803 it became the 35th [Sussex] Regiment of Foot. So for a few years after 1803 you may still see reference to Dorsetshire. Another thing about regiments and wives abroad is that quite often the husband or wife could die from disease, accident etc., and it was quite common for widows and widowers or single soldiers and widowers to marry, so keep an open mind but beware jumping to conclusions.