Would people in West Africa have had domesticated plants or animals that far back?

Not only would they have had domesticated plants and animals that far back, they domesticated quite a few themselves.

Pearl millet (Pennisetum glaucum) was one of the most important staples of the ancient world, and it was domesticated in West Africa by around 2,500 BC. The oldest domesticated grains of pearl millet known today are from Ghana in West Africa, with radiocarbon dates of around 1,800 BC. By the period you mention, pearl millet was the single most important staple cereal across all of West Africa, including Gambia. In fact, since you mention Gambia, it would have been even more important there, because the closer you get to the Sahara, pearl millet becomes more significant because of its ability to thrive in dry conditions.

Rice has three independent domestication events – in southeast Asia-China, in India, and in West Africa (for the 3 main varieties: Oryza japonica, Oryza indica and Oryza glaberrima). Genetic evidence shows that African rice - Oryza glaberrima - was domesticated in West Africa along the banks of the Niger river right around the period you asked about. Rice formed a very important part of West African economies until very late. Portuguese explorers who visited the West Coast of Africa during the 16th century wrote about huge rice fields spanning both sides of the rivers they navigated into the African continent. One reason why slaves from West Africa were preferred in the southern colonies was because they already knew how to grow rice.

Sorghum, in particular Sorghum bicolor was domesticated in a belt stretching from Mauretania in the west to Ethiopia in the east, and was widely grown in West Africa by the second millennium BC.

Aside from cereals, some species of bottle gourds were first domesticated in west and sub-Saharan Africa, in particular, Lagenaria siceraria, spp siceraria, the white flowered gourd. This was also over 4,000 years ago, so it may well fall into the period you’re interested in. Other plants domesticated in Africa include watermelons (around 5,000 years ago in Namibia), Bambara groundnuts (Vigna subterranea) in West Africa, cowpeas in West Africa, yams in sub-Saharan Africa around 5,000 years ago.

This is just a list of plants domesticated in or near West Africa. In addition, there were plenty of other old world crops domesticated elsewhere in Asia or the Middle East, that were also grown in West Africa.

Africa has contributed less to animal domestication, mostly the donkey (Equus asinus) in Nubia around 5,000 years ago and the guinea fowl (Meleagris galeata) in West Africa, also around 5,000 years ago. Neither became an important food source. But animals used for food (cows, sheep, goats) began entering Africa through Egypt beginning around 9,000 years ago, and over the next 4,000 – 5,000 years spread pretty much all over Africa where the ecosystem could support pastoralism.

Generally speaking, agriculture and animal husbandry became more prevalent in West Africa beginning slightly over 4,000 years ago, as the Sahara continued to dry and populations were forced southwards. They followed the upper Niger river valley, and its tributaries, particularly the Senegal river valley. Agriculture seems to have been the province of the Niger-Congo speakers, while animal husbandry was brought by Nilo-Saharan speakers, but over time the Nilo-Saharans were absorbed. Archeological sites such as those in Ghana show that agriculture began at the fringes of the rain forest and was supplemented by food gathered from the rain forest, as well as by herding. Some products of the rain forest were also later domesticated (such as okra, kola, melegueta peppers), but it’s hard to say if they were of any significance in 1250 BC.