Baxter won his two previous caps in July, coming on as a half-time substitute in England’s 16-15 defeat against New Zealand before making his first start in a 24-17 loss against the same opposition the following week.
England face New Zealand, Australia, South Africa and Japan in the autumn internationals next month.
“For him to go from [Quins matches against] Sarries, to Bath and be involved with the England setup is a lot for a young man,” Wilson said.
“But he’s a young man who I think will take it in his stride.”
Quins take on last season’s runners up Bath at The Stoop with two wins and two defeats from their first four games.
Bath have won three matches and have lost once and Wilson said his players will need to be wary of the carrying power of players including Alfie Barbeary and Ollie Lawrence, on top of the running and kicking talents the team possess.
“We want to show [last weekend’s victory over Saracens] isn’t a one-off,” he said.
“The biggest factor is The Stoop, the fans make the difference.
“We’re very lucky with what we have there, it’s a packed house and we know they’re great occasions, the boys love playing at The Stoop.”
